jquery-ui-datepicker-fixed-position-patch.js

const checkOffset = $.datepicker._checkOffset;

$.extend($.datepicker, {
    _checkOffset: function(inst, offset, isFixed) {
        if(!isFixed) {
            return checkOffset.apply(this, arguments);
        }

        let isRTL = this._get(inst, "isRTL");
        let obj = inst.input[0];

        // copied from Datepicker._findPos (node_modules/jquery-ui/datepicker.js)
        while (obj && (obj.type === "hidden" || obj.nodeType !== 1 || $.expr.filters.hidden(obj))) {
            obj = obj[isRTL ? "previousSibling" : "nextSibling"];
        }

        let rect = obj.getBoundingClientRect();

        return {
            top: rect.top,
            left: rect.left,
        };
    }
});

Hello, your script saved my life. But I made a little correction because it is necessary to take into account the height of the input.

const checkOffset = $.datepicker._checkOffset;

$.extend($.datepicker, {
    _checkOffset: function(inst, offset, isFixed) {
        if(!isFixed) {
            return checkOffset.apply(this, arguments);
        }

        let isRTL = this._get(inst, "isRTL");
        let obj = inst.input[0];

        // copied from Datepicker._findPos (node_modules/jquery-ui/datepicker.js)
        while (obj && (obj.type === "hidden" || obj.nodeType !== 1 || $.expr.filters.hidden(obj))) {
            obj = obj[isRTL ? "previousSibling" : "nextSibling"];
        }

        let rect = obj.getBoundingClientRect();

        return {
            top: rect.top+rect.height,
            left: rect.left
        };
    }
});