  A study of spinless matter fermions coupled to a constrained $\mathbb{Z}_{2}$
lattice gauge theory on a triangular ladder is presented. The triangular unit
cell and the ladder geometry strongly modify the physics, as compared to
previous analysis on the square lattice. In the static case, the even and odd
gauge theories for the empty and filled ladder are identical. The gauge field
dynamics due to the electric coupling is drastically influenced by the absence
of periodic boundary conditions, rendering the deconfinement-confinement
process a crossover in general and a quantum phase transition (QPT) only for
decorated couplings. At finite doping and in the static case, a staggered flux
insulator at half filling and vanishing magnetic energy competes with a uniform
flux metal at elevated magnetic energy. As for the square lattice, a single QPT
into a confined fermionic dimer gas is found versus electric coupling. Dimer
resonances in the confined phase are however a second order process only,
likely reducing the tendency to phase separate for large magnetic energy. The
results obtained employ a mapping to a pure spin model of $\mathbb{Z}_{2}$
gauge-invariant moments, adapted from the square lattice, and density matrix
renormalization group calculations thereof for numerical purposes. Global scans
of the quantum phases in the intermediate coupling regime are provided.
