In this paper, we introduce the notion of Mehler–Fock Wigner distribution and examine the underlying theory of Toeplitz operators. Particularly, we study the trace class properties of such operators and also demonstrate that they belong to the Schatten–von Neumann class. Nonetheless, special attention is paid to the boundedness and compactness of the Toeplitz operators associated with the Mehler–Fock Wigner distribution on (Formula presented.), (Formula presented.).