  The present paper analyze the constraints on the confluent Heun
type-equation,
$(a_{3,1}r^2+a_{3,2}r)y"+(a_{2,0}r^2+a_{2,1}r+a_{2,2})y'-(\tau_{1,0}r+\tau_{1,1})y=0,$
where $|a_{3,1}|^2+|a_{3,2}|^2\neq 0, $ and $a_{i,j},i=3,2,1, j=0,1,2$ are real
parameters, to admit polynomial solutions. The necessary and sufficient
conditions for the existence of these polynomials are given. A three-term
recurrence relation is provided to generate the polynomial solutions
explicitly. We, then, prove that these polynomial solutions are a source of
finite sequences of orthogonal polynomials. Several properties, such as the
recurrence relation, Christoffel-Darboux formulas and the moments of the weight
function, are discussed. We also show a factorization property of these
orthogonal polynomials that allow for the construction of other sequences of
orthogonal polynomials. For illustration, we examines the quasi- exactly
solvability of the $(p,q)$-hyperbolic potential
$V(r)=-V_0\sinh^p(r)/\cosh^q(r), V_0>0, p\geq 0, q>p$. The associated
orthogonal polynomials generated by the solutions of the Schr\"odinger equation
with the $(4,6)$-hyperbolic potential are constructed.
