In Photoshop using Type Tool>>insert date if any shortcut or function keys?

In CC2018, you can create such a script.

Assign a hotkey to it.

Before editing the text, call the script. It will copy the date value to the clipboard.

While editing the text just in the right place, press Ctrl+V

var d = Date().split(" ");
var m = "00";
switch (d[1])
    {
    case "Jan": m = "01"; break;
    case "Feb": m = "02"; break;
    case "Mar": m = "03"; break;
    case "Apr": m = "04"; break;
    case "May": m = "05"; break;
    case "Jun": m = "06"; break;
    case "Jul": m = "07"; break;
    case "Aug": m = "08"; break;
    case "Sep": m = "09"; break;
    case "Oct": m = "10"; break;
    case "Nov": m = "11"; break;
    case "Dec": m = "12"; break;
    }
var desc = new ActionDescriptor();
desc.putString(stringIDToTypeID("textData"), d[2] + "." + m + "."+ d[3]);
executeAction(stringIDToTypeID("textToClipboard"), desc, DialogModes.NO);
alert(d[2] + "." + m + "."+ d[3] + "\nwas copied to the clipboard", "Warning") 

Moving to Photoshop Scripting​

That task could be automated with a Script.

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Photoshop Scripting