In this manuscript, the techniques for finding the solutions in terms of (γ,δ)- Jacobsthal and (γ,δ)- Jacobsthal Lucas sequences for two distinct categories of the Diophantine equations U2n – (p2+q) v2n= q2n and U2 n– (4p2q2 -8) v2n = (-2δ)n , n>1, δ∈Z- {0} where p and q are specialised prime numbers, including Gaussian prime, Good prime, Lucky prime, Chen prime and Circular prime are offered. Moreover, the entire solutions discovered are confirmed with the assistance of three distinct Python codes.