In most articles I have seen that derivation is only done to the first order correction in the energy eigenvalues for the case of time independent degenerate perturbation.
If the first-order calculation in a degenerate perturbation theory (relative to a free smallness order parameter) is understood, the higher-order ones can also be achieved in a similar fashion.
In the present case, retain all the second-order terms and repeat the that procedure followed before.
Thank you P. K. Karmakar sir for your help.... I have already did an derivation but verify whether I have done correctly or not I wanted to check whether I have done correctly or not.... I have through gone reference material suggested by you but I exactly didn't found the solution related to the problem....