  We construct an exact black hole solution for the Einstein gravity coupled
with the nonlinear electrodynamics (which corresponds to the Maxwell
electrodynamics in the weak field limit) in the presence of a cloud of strings
as the source. We study the thermodynamical properties of the black hole
solutions and derive the corrected first-law of thermodynamics. The presence of
a cloud of strings does not affect the stability of the present black hole.
However, a second-order phase transition exists for this system at a critical
horizon radius. Furthermore, we study the quasinormal modes and their shadow
radius. In addition, we find that, upon variation, the parameters of the theory
show different aspects of the optical characteristics of the black hole
solutions.
