if you need 144 hz just use more lattop
144/60 = 2.4 so you need 2.4 laptop ?
google is your friend. HDMI 3 (I think?) will support 144Hz but HDMI2 won't. no idea and Mini DP compatibility
if your laptop gpu supports 144hz then the mini-dp should do the trick.
(hdmi doesnt support 144hz)
mDP supports 144hz, my old graphics card had an mDP but my monitor only had a DP, so I used an mDP -> DP adapter and 144hz worked fine @ 1920x1080.
EDIT: HDMI can support up to 120hz @ 1024x768 fyi.