  In this manuscript, new algebraic and analytic aspects of the orthogonal
polynomials satisfying $R_{II}$ type recurrence relation given by
\begin{align*} \mathcal{P}_{n+1}(x) = (x-c_n)\mathcal{P}_n(x)-\lambda_n
(x-a_n)(x-b_n)\mathcal{P}_{n-1}(x), \quad n \geq 0, \end{align*} where
$\lambda_n$ is a positive chain sequence and $a_n$, $b_n$, $c_n$ are sequences
of real or complex numbers with $\mathcal{P}_{-1}(x) = 0$ and $\mathcal{P}_0(x)
= 1$ are investigated when the recurrence coefficients are perturbed.
Specifically, representation of new perturbed polynomials (co-polynomials of
$R_{II}$ type) in terms of original ones with the interlacing and monotonicity
properties of zeros are given. For finite perturbations, a transfer matrix
approach is used to obtain new structural relations. Effect of co-dilation in
the corresponding chain sequences and their consequences onto the unit circle
are analysed. A particular perturbation in the corresponding chain sequence
called complementary chain sequences and its effect on the corresponding
Verblunsky coefficients is also studied.
