On the Maillet–Baker Ruban Continued Fractions in the $p$-Adic Field

We establish a transcendence criterion for a class of quasi-periodic Ruban $p$-adic continued fractions. We prove that a $p$-adic number whose partial quotients sequence is quasi-periodic and bounded in the $p$-adic field $\mathbb{Q}_p$ is either quadratic or transcendental.