We study the scenario of Kaniadakis horizon-entropy cosmology, which arises from the application of the gravity-thermodynamics conjecture using the Kaniadakis modified entropy. The resulting modified Friedmann equations contain extra terms that constitute an effective dark energy sector. We use data from cosmic chronometers, Type Ia supernova, H ii galaxies, strong lensing systems, and baryon acoustic oscillation observations, and we apply a Bayesian Markov chain Monte Carlo analysis to construct the likelihood contours for the model parameters. We find that the Kaniadakis parameter is constrained around 0, namely around the value where the standard Bekenstein-Hawking is recovered. Concerning the normalized Hubble parameter, we find h=0.708+0.012-0.011, a result that is independently verified by applying the H0(z) diagnostic and, thus, we conclude that the scenario at hand can alleviate the H0 tension problem. Regarding the transition redshift, the reconstruction of the cosmographic parameters gives zm T=0.715+0.042-0.041. Furthermore, we apply the Akaike, Bayesian, and deviance information criteria, and we find that in most data sets the scenario is statistical equivalent to Λ cold dark matter one. Moreover, we examine the big bang nucleosynthesis, and we show that the scenario satisfies the corresponding requirements. Additionally, we perform a phase-space analysis, and we show that the Universe past attractor is the matter-dominated epoch, while at late times the Universe results in the dark-energy-dominated solution. Finally, we show that Kaniadakis horizon-entropy cosmology accepts heteroclinic sequences, but it cannot exhibit bounce and turnaround solutions.
