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We explore the cosmological aspects of interacting Tsallis holographic darkenergy (THDE) in a $q$-modified DGP braneworld setup emerging from non-Gaussianstatistical mechanics.To this end, three classes of superstatistics, that is,log-normal, inverse $\chi^2$ and $\chi^2$ superstatistics were incorporatedinto the model. We examined the implication of the three superstatistics ondifferent cosmological parameters, namely, the dimensionless energy density andthe equation-of-state (EoS) of THDE, along with the deceleration parameter andthe squared speed of sound. As a result, we noted that the cosmologicalparameters stemming from the $\chi^2$ superstatistics, with a parameter $q >1$, represent the highest deviation from those ascribed to the standard DGPmodel. While the system parameters show appropriate behavior in all threecases, the model cannot achieve stability throughout the history of theUniverse. It is probably the outcome of setting the Hubble horizon as theinfrared cutoff. Furthermore, the behavior of EoS was found to be governed bythe value of the THDE parameter ${\delta}$. That is to say, for ${\delta} > 2$THDE exhibits a phantom-like behavior while for ${\delta} < 2$ it displays aquintessence behavior. Constrained by the dominant energy condition, an upperbound on ${\delta}$ $({\delta} < 2)$ has been imposed.

Interacting Tsallis holographic dark energy in $q$-modified DGP braneworld