Baj seems to be correct, it is next to Tata, but also close to Budapest, maybe 40 minutes drive. I have searched in an old forum which is closed now, back in 2008 someone mentioned tha he is from the Bertalan family in Baj, but relatives were from Biharugra. In the marriage registers till 1930 i did not find any Bertalan, nor in the old church books, so it is very probable that the family moved there from somewhere else. In Biharugra an in thst area the name is more common. They majority of the people there are protestants or baptists.
