 Thermodynamics suggests that gravity and entropy are connected, which implies that modifying the entropy expression will modify the field equations. Considering the modified Barrow entropy associated with the apparent horizon alters the Friedman equations. The modified HDE model with Barrow entropy leads to different energy densities and modified Friedman equations. Furthermore, the Hubble horizon and future event horizon act as infrared cutoffs, and their effects on the cosmology depend on the value of the Barrow exponent. When the Barrow exponent is large, the Eos parameter can cross the phantom line, while when it is small, the deceleration parameter is shifted and the time of universe phase transition is delayed. This article was authored by Ahmad Shiki and Meryl Sahibi-Hammadan.