What pen is used to write the signature on the back of the soft pen competition?

This is not allowed! Marker is not a soft pen, but calligraphy works belong to the category of soft pen calligraphy. You can sign in different fonts, but you can't use markers! What a layman! I guess you might want to write the signature in a smaller font, which is different from the text. You can write with a pen tip, and the font will naturally be smaller! Or, try a smaller brush.