We develop two functional models for closed isometric entire operators V with finite deficiency indices (p, p) acting in a separable Pontryagin space \({{\mathcal {K}}}\) . In the first functional model it is shown that every such operator V is unitarily equivalent to a restriction \(T^{{\mathfrak {E}}}\) of the backward shift operator in the de Branges-Pontryagin space \({{\mathcal {B}}}({{\mathfrak {E}}})\) of \(p\times 1\) vector valued entire functions. The second functional model is used to parametrize a class of compressed coresolvents of extensions \({{\widetilde{V}} }\) of V in terms of the range of a linear fractional transformation that is associated with the model. These results are applied to obtain a description of the set of solutions of an indefinite truncated trigonometric moment problem.
