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When the co-recursion and co-dilation in the recurrence relation of certainsequences of orthogonal polynomials are not at the same level, the behaviour ofthe modified orthogonal polynomials is expected to have different propertiescompared to the situation of the same level of perturbation. This manuscriptattempts to derive structural relations between the perturbed and original$R_{II}$ type orthogonal polynomials. The classical result is improved using atransfer matrix approach. It turns out that the $R_{II}$ fraction withperturbation is the rational spectral transformation of the unperturbed one.The derived notions are used to deduce some consequences for the polynomialsorthogonal on the real line. A quadrature rule is formulated from the perturbed$R_{II}$ type recurrence, leading to observations that are based on numericalresults.

Generalized co-polynomials of $R_{II}$ type and associated quadrature rules