In this paper we establish several recurrence relations about Euler-Apéry type multiple zeta star values and a parametric variant of it by using the method of iterated integrals. Then using the formulas obtained, we find the explicit evaluations for some specific Euler-Apéry type multiple zeta star values and one of its parametric variant, and Euler-Apéry type multiple $t$-star values.

arXiv admin note: text overlap with arXiv:2103.01377