  We obtain Schwarz-Pick lemma for $(\alpha, \beta)$-harmonic functions u in
the disc, where $\alpha$ and $\beta$ are complex parameters satisfying $\Re
\alpha + \Re \beta > -1$. We prove sharp estimate of derivative at the origin
for such functions in terms of $L^p$ norm of the boundary function. Also, we
give asymptotically sharp estimate of the norm of the derivative at point $z$
in the unit disc. These estimates are extended to higher order derivatives. Our
results extend earlier results for $\alpha$-harmonic and $T_\alpha$-harmonic
functions.
