  We prove interior boundedness and H\"{o}lder continuity for the weak
solutions of nonlocal double phase equations in the Heisenberg group
$\mathbb{H}^n$. This solves a problem raised by Palatucci and Piccinini et. al.
in 2022 and 2023 for nonlinear integro-differential problems in the Heisenberg
group $\mathbb{H}^n$. Our proof of the a priori estiamtes bases on the spirit
of De Giorgi-Nash-Moser theory, where the important ingredients are
Caccioppoli-type inequality and Logarithmic estimate. To achieve this goal, we
establish a new and crucial Sobolev-Poincar\'{e} type inequality in local
domain, which may be of independent interest and potential applications.
