The evolution of plasma in fusion devices is non-uniform and local physics, such as pellet injections, heating, and magnetic islands must be finely resolved for accurate simulations. Existing geometric particle-in-cell (PIC) methods on structured grids are primarily based on tensor product finite element spaces [1] or mimetic finite differences on translation-invariant grids [2]. Consequently, these methods are not easily adaptable to non-uniform meshes and complex geometries. To enable efficient large-scale simulations, we propose a geometric PIC scheme on locally refined meshes. Field discretization is based on broken-FEEC (Finite Element Exterior Calculus) [3] in a strong Faraday form and the distribution function is approximated by a sum of Dirac delta particles. The resulting semi-discrete equations form a non-canonical Hamiltonian system. Poisson or Hamiltonian splitting schemes are applied to obtain energy- or Gauss-preserving time integrators, respectively. In case of linear finite elements, mass lumping can be employed to make certain variants of the scheme fully explicit and well suited for high performance computing. However, the global CFL condition is governed by the finest mesh. For the unconditionally stable implicit schemes, the solver iterations do not directly involve the particles and system sizes are manageable. The algorithms are implemented in the GEMPICX C++ code, which is based on the AMReX framework [4]. This framework handles mesh generation and enables scalability and performance portability across various platforms, including both CPU and GPU architectures.