This paper is devoted to analyzing the consequence of the presence of a scalar field on the statistical properties of the hairy
black holes in 2+1 dimensions. The presence of the scalar field
can be related to the fluctuations of thermal effects. Consequences of the entropy and temperature corrections, on the
statistical characteristics of the black holes investigated. Different
types of hairy black holes are considered and their modified
thermodynamics quantities are calculated up to the first-orders
corrections. The model has some novel outcomes on the P − V
plane of space and its features as the phase shifts and critical
points. These significant effects are studied, and special attention
is paid to checking the local and global steadiness of the black
holes under the applied conditions. The influences of the model
on the related thermodynamic characteristics are obtained and
explained