Self-defined point type and independent point color setting is required, e.g.

plot 'data'  w lp lt 1 lc 1 pt "H" font 'Times'  ps 0.5 pc 3


set pointtype 3 "H" font "times" tc rgb "blue"

Although "with labels" can partly fulfill this request, it does not support "linepoint" and does not display legends as point or linepoint.