页面代码：

        <div class="layui-form-item" style="margin-left: 10px">
            <div class="layui-inline layui-form">
                <label class="layui-inline" id="worldlable" style="width: 200px; height:30px">
                    <input id="worldId" type="text" class="layui-input laydate-test" data-type="date"
                        autocomplete="off">
                </label>
                <div class="layui-input-inline" style="width: 100px; height:30px">
                    <select name="type" id="selectedOption" lay-filter="college">
                        <option value="day" selected="selected">按日</option>
                        <option value="week" selected="selected">按周</option>
                        <option value="month">按月</option>
                        <option value="quarter">按季度</option>
                        <option value="year">按年</option>
                    </select>
                </div>
            </div>
        </div>

JS代码：

        layui.use(['form', 'upload', 'layer', 'laydate', 'jquery'], function () {
            let form = layui.form;
            let layer = layui.layer;
            let laydate = layui.laydate;
            laydate.render({
                elem: '#worldId',
                theme: '#70c2ff',//将控件颜色修改为蓝色
                max: genTime('day'),//如不需要限制可选时间为当前时间，可将此行注释
                value: genTime('day'),
                type: 'date'
            });
            form.on('select(college)', function (data) {
                let opt = $("#selectedOption").val();
                let ele = $("#selectedOption");
                $("#worldId").remove();
                $("#worldlable").html('<input id="worldId" type="text" class="layui-input laydate-test" data-type="date" autocomplete="off">');
                // 月
                if (opt == "month") {
                    laydate.render({
                        elem: '#worldId',
                        theme: '#70c2ff',//将控件颜色修改为蓝色
                        type: 'month',
                        max: genTime('month'),
                        value: genTime('month'),
                        btns: ['clear', 'confirm']
                    });
                    // 日
                } else if (opt == "day") {
                    laydate.render({
                        elem: '#worldId',
                        theme: '#70c2ff',//将控件颜色修改为蓝色
                        type: 'date',
                        max: genTime('day'),
                        value: genTime('day'),
                        btns: ['clear', 'confirm']
                    });
                    // 周
                } else if (opt == "week") {
                    renderWeekDate('#worldId', '');
                }// 季度
                else if (opt == "quarter") {
                    renderSeasonDate('#worldId', '');
                    // 年
                } else if (opt == "year") {
                    laydate.render({
                        elem: '#worldId',
                        theme: '#70c2ff',//将控件颜色修改为蓝色
                        type: 'year',
                        max: genTime('day'),
                        value: genTime('year'),
                        btns: ['clear', 'confirm']
                    });
                }
            });
            // 周
            function renderWeekDate(ohd, sgl) {
                let ele = $(ohd);
                laydate.render({
                    elem: ohd,
                    theme: '#70c2ff',//将控件颜色修改为蓝色
                    type: 'date',
                    max: genTime('day'),
                    format: "yyyy-MM-dd~yyyy-MM-dd",
                    btns: ['clear', 'confirm'],
                    done: function (value, date, endDate) {
                        if (value != "" && value.length > 0) {
                            let today = new Date(value.substring(0, 10));
                            let weekday = today.getDay();
                            let monday;
                            let sunday;
                            if (weekday == 0) {
                                monday = new Date(1000 * 60 * 60 * 24 * (weekday - 6) + today.getTime());
                            } else {
                                monday = new Date(1000 * 60 * 60 * 24 * (1 - weekday) + today.getTime());
                            }
                            if (weekday == 0) {
                                sunday = today;
                            } else {
                                sunday = new Date(1000 * 60 * 60 * 24 * (7 - weekday) + today.getTime());
                            }
                            let month = monday.getMonth() + 1;
                            if (month < 10) {
                                month = "0" + month;
                            }
                            let day1 = monday.getDate();
                            if (day1 < 10) {
                                day1 = "0" + day1;
                            }
                            let start = "" + monday.getFullYear() + "-" + month + "-" + day1;
                            let month2 = sunday.getMonth() + 1;
                            if (month2 < 10) {
                                month2 = "0" + month2;
                            }
                            let day2 = sunday.getDate();
                            if (day2 < 10) {
                                day2 = "0" + day2;
                            }
                            let end = "" + sunday.getFullYear() + "-" + month2 + "-" + day2;
                            ele.val(start + "~" + end);
                        } else {
                            ele.val('');
                        }
                    }
                });
            }
            // 季度
            function renderSeasonDate(ohd, sgl) {
                let ele = $(ohd);
                laydate.render({
                    elem: ohd,
                    theme: '#70c2ff',//将控件颜色修改为蓝色
                    type: 'month',
                    format: 'yyyy-M',
                    btns: ['clear', 'confirm'],
                    ready: function (value, date, endDate) {
                        let hd = $("#layui-laydate" + ele.attr("lay-key"));
                        if (hd.length > 0) {
                            hd.click(function () {
                                quarter($(this));
                            });
                        }
                        quarter(hd);
                    },
                    done: function (value, date, endDate) {
                        if (!isNull(date) && date.month > 0 && date.month < 5) {
                            ele.attr("startDate", date.year + "-" + date.month);
                        } else {
                            ele.attr("startDate", "");
                        }
                        if (!isNull(endDate) && endDate.month > 0 && endDate.month < 5) {
                            ele.attr("endDate", endDate.year + "-" + endDate.month)
                        } else {
                            ele.attr("endDate", "");
                        }
                    }
                });
            }
            });
           function genTime(opt) {
            let now = new Date();
            let year = now.getFullYear();
            let mth = now.getMonth();
            let day = now.getDate();
            let month = mth + 1;
            if (month < 10) {
                month = '0' + month
            }
            if (day < 10) {
                day = '0' + day
            }
            let str;
            if (opt == 'day') {
                str = year + '-' + month + '-' + day;
            } else if (opt == 'month') {
                str = year + '-' + month;
            }
            return str;
        }
        function quarter(thiz) {
            let mls = thiz.find(".laydate-month-list");
            mls.each(function (i, e) {
                $(this).find("li").each(function (inx, ele) {
                    let cx = ele.innerHTML;
                    if (inx < 4) {
                        ele.innerHTML = cx.replace(/月/g, "季度");
                    } else {
                        ele.style.display = "none";
                    }
                });
            });
        }
        function isNull(quarter) {
            if (quarter == null || typeof (quarter) == "undefined" || quarter == "") return true;
            return false;
        }
        /**
         * 日期转为周 格式2020-07-14
         * @param {String} dateString 日期
        */
        function getYearWeek(dateString) {
            let da = dateString;//日期格式2015-12-30
            //当前日期
            let date1 = new Date(da.substring(0, 4), parseInt(da.substring(5, 7)) - 1, da.substring(8, 10));
            //1月1号
            let date2 = new Date(da.substring(0, 4), 0, 1);
            //获取1月1号星期（以周一为第一天，0周一~6周日）
            let dateWeekNum = date2.getDay() - 1;
            if (dateWeekNum < 0) { dateWeekNum = 6; }
            if (dateWeekNum < 4) {
                //前移日期
                date2.setDate(date2.getDate() - dateWeekNum);
            } else {
                //后移日期
                date2.setDate(date2.getDate() + 7 - dateWeekNum);
            }
            let d = Math.round((date1.valueOf() - date2.valueOf()) / 86400000);
            if (d < 0) {
                let date3 = (date1.getFullYear() - 1) + "-12-31";
                return getYearWeek(date3);
            } else {
                //得到年数周数
                let year = date1.getFullYear();
                let week = Math.ceil((d + 1) / 7);
                return year + "-" + week;
            }
        }
 

效果如下图所示：