APPLIED NEW TAN NO BUT SUB CATEGORY GOES WORNG AS HINDU UNDIVIDED FAMILIY

You need to file TAN correction / change request, not a fresh TAN application. Official TAN correction allows change of category of applicant if the TAN database is showing the wrong category. Since your partnership firm is appearing as HUF, apply for TAN correction from HUF to Firm and verify PAN/entity type/AO code once again. TRACES correction is for TDS return data, not for changing TAN master category.