The following
set xdata time
set timefmt '%d-%m-%Y'
set xtics add ('Jan', '15-01-2026')
plot '-' using (timecolumn(1)):2 with lines
01-01-2026 1
31-12-2026 2
e
adds a tic labelled '15/01/26' (the default format) in the middle of january, when I would expect 'Jan' there.
(gnuplot 6.0 patchlevel 5 on Windows)
The problem here is an extra comma in the "set xtics" command. The format of the command is
set ("label1" place1, "label2" place2, ...)
Change your command to
set xtics add ('Jan' '15-01-2026') # no comma