  In this paper, we investigate a recent proposed model - so called the Tsallis
holographic dark energy (THDE) model. In this case, we consider the
non-gravitational and phenomenological interaction between dark sectors. We fit
the free parameters of the model using Pantheon Supernovae Type Ia data, Baryon
Acoustic Oscillations, Cosmic Microwave Background, Gamma-Ray burst and the the
local value of the Hubble constant. We examine the THDE model to check its
compatibility with observational data using objective Information Criterion
(IC). We find that the THDE model cannot be supported by observational data.
Using the Alcock-Paczynski (AP) test we check the deviation of the model
compared to $\Lambda$CDM. Surveying the evolution of squared of sound speed
$v^2_s$ as an another test we check the stability of the interacting and
non-interacting THDE models. In addition, using the modified version of the
CAMB package, we observe the suppressing the CMB spectrum at small K-modes and
large scale.
