what kind of name is kuzma
Your Kuzma or Kuzmiak ancestors were Rusyns. Your ancestral surname Kuzma is Rusyn version of name Cosmas and it was pretty common given name among Rusyns. Saints Cosmas and Damian were early Christian martyrs FYI. Rusyn version of Damian is Demjan and it was very common Rusyn given name which became by time surname.