How does the choice of blood draw site influence the possible specificity of a serological test?
This ref, https://academic.oup.com/ajcp/article/144/6/885/1761216
show that drops of finger prick blood vary more than venous blood.

The main reason for using venous blood is licensing. A test is licensed only for an exact procedure and materials. If you vary any conditions the license is invalid.

However, I would not expect a test for antibodies (present vs. absent) to show much variation except for detecting the lowest levels of antibodies. (Sorry I cannot find a ref for this).