  The goal of this paper is to study conformal Yamabe soliton and $*$-Yamabe
soliton, whose potential vector field is torse forming. Here, we have
characterized conformal Yamabe soliton admitting potential vector field as
torse forming with respect to Riemannian connection, semi-symmetric metric
connection and projective semi-symmetric connection on Riemannian manifold. We
have also shown the nature of $*$-Yamabe soliton with torse forming vector
field on Riemannian manifold admitting Riemannian connection. Lastly we have
developed an example to corroborate some theorems regarding Riemannian
connection on Riemannian manifold.
