As I see it, Baselland is responsible only for processing and refunding source-tax for the period in which the taxpayer lived in Baselland. This would mean that a separate application for a new assessment of the source-tax for Basel-Stadt should be made separately. Unfortunately, the "Antragsformular für Tarifkorrektur und Rückerstattung der Verrechnungs-steuer CH" for 2019 for Basel-Stadt was due by 30 September 2020:


https://www.steuerverwaltung.bs.ch/s...formulare.html


Suggestion: although the submission deadline for 2019 has been missed, consider completing the Antragsformular for Basel-Stadt anyway, attaching the required supporting document but also including a copy of the Baselland submission. With some luck the Basel-Stadt tax office might accept it. If they don't, you're just out a small amount of your time and the price of a stamp.