To Whom This May Concern:
There is a yDNA haplogroup associated with the patriline of R' Betzalel. For those interested in using the haplogroup to establish a descent from this lineage, please see the document in the https://www.geni.com/projects/Rabbinical-Lineages-yDNA-and-Haplogro..., available through the photos and documents page.
Private User Thanks for your inquiry. You need to have a yDNA test obtained from a person who you think descends from the same patriline (a patriline ("father line") is a person's ancestry traced only through related males) as Betzalel ben Chaim. This test is offered by FTDNA and is called 'Paternal Ancestry' (https://www.familytreedna.com/products/y-dna#/compare) There are three testing levels and one may use the least costly level in order to determine whether there is sufficient evidence to continue on to the higher levels.