We explore transposed Poisson structures on the Lie algebra: the deformed twisted Schrödinger-Virasoro algebra D(λ), as well as two Lie superalgebras: the super-BMS3 algebra and the twisted N=1 Schrödinger-Neveu-Schwarz algebra. Initially, we demonstrate the absence of non-trivial transposed Poisson structures on the Lie algebra D(λ) for λ≠1 and provide an example of a transposed Poisson algebra with associative and Lie parts isomorphic to the algebra of triadic extended Laurent polynomials and D(1). Subsequently, we establish that the super-BMS3 algebra possesses non-trivial 12-superderivations but lacks a non-trivial transposed Poisson structure. Finally, we prove that the twisted N=1 Schrödinger-Neveu-Schwarz algebra does not have non-trivial 12-superderivations and thus lacks non-trivial transposed Poisson structures.