Verma Bases for finite dimensional Representations of the orthosymplectic Lie superalgebra $\mathfrak{s}\mathfrak{p}\mathfrak{o}(4\mathrm{\mid }1)$

We define the Verma vector system for each finite dimensional irreducible representation of the orthosymplectic Lie superalgebra $\mathfrak{s}\mathfrak{p}\mathfrak{o}(4\mathrm{\mid }1)$ with the highest weight $\lambda ,$ via the conditions that making a tableau with shape $\lambda$ to be a Kashiwara-Nakashima tableau. We then show the linearly independence of this vector system. It turns out to be a basis of the finite dimensional irreducible representation $L(\lambda )$ of the orthosymplectic Lie superalgebra $\mathfrak{s}\mathfrak{p}\mathfrak{o}(4\mathrm{\mid }1)$ with the highest weight $\lambda ,$ which analogs to the Verma basis of representations of ${\mathfrak{s}\mathfrak{p}}_4,$ called the Verma basis of the finite dimensional irreducible representation of $\mathfrak{s}\mathfrak{p}\mathfrak{o}(4\mathrm{\mid }1)$.