  S. Ovsienko proved that the Gelfand-Tsetlin variety for $\mathfrak{gl}_n$ is
equidimensional (i.e., all its irreducible components have the same dimension)
of dimension $\frac{n(n-1)}{2}$. This result is known as Ovsienko's Theorem and
it has important consequences in Representation Theory of Algebras. In this
paper, we will study the Gelfand-Tsetlin varieties for restricted Yangian
$Y_p(\mathfrak{gl}_n)$ and the equidimensionality for $Y_p(\mathfrak{gl}_3)$.
