  We construct asymptotically flat, static spherically symmetric black holes
with regular centre in $f(R,T)$ gravity coupled to nonlinear electrodynamics
Lagrangian. We obtain generalized metric function of the Bardeen and Hayward
black holes. The null, weak and strong energy conditions of these solutions are
discussed. All the energy conditions hold outside the black hole's outer event
horizon by appropriated choices of parameters. Quasinormal mode of massive
scalar perturbation is also investigated. Quasinormal frequencies are computed
via the sixth order Wentzel-Kramers-Brillouin (WKB) with Pad\'e approximation.
All the imaginary parts of the frequencies are found to be negative. Finally,
we provide an analysis in the eikonal limit.
