  We consider the entanglement island in a deformed Jackiw-Teitelboim black
hole in the presence of the phase transition. This black hole has the van der
Waals-Maxwell-like phase structure as it is coupled with a Maxwell field. We
study the behavior of the Page curve of this black hole by using the island
paradigm. In the fixed charge ensemble, we discuss different situations with
different charges that influence the system's phase structure. There is only a
Hawking-Page phase transition in the absence of charges, which leads to an
unstable small black hole. Hence, the related Page curve does not exist.
However, a van der Waals-Maxwell-like phase transition occurs in the presence
of charges. This yields three black hole solutions. The Page curve of the
middle size black hole does not exist. For the extremal black hole, the Page
time approaches zero in the phase transition situation but becomes divergent
without the phase transition. In a word, we study the Page curve and the island
paradigm for different black hole phases and in different phase transition
situations.
