I read the answer from @Ramillies, the document is comprehensive but I did not figure out how to use the commands correctly. Then I found a very simple example in the doc page Expressive marks attached to notes.

Now this vertical stack of markups is exactly what I want:

My source code:

...
%% fingering symbols
fngaLong = \finger\markup{\box{\pad-markup #0.2 \override #'(font-name . "pipa") \fontsize #7 "a-"}}
...
\appoggiatura{c8-3\startTrillSpan^\fngaLong} a2-1
c8\stopTrillSpan d4\fermata c8

I read the answer from @Ramillies, the document is comprehensive but I did not figure out how to use the commands correctly. Then I found a very simple example in the doc page Expressive marks attached to notes.

Now this vertical stack of markups is exactly what I want:

My source code:

...
%% fingering symbols
fngaLong = \finger\markup{\box{\pad-markup #0.2 \override #'(font-name . "pipa") \fontsize #7 "a-"}}
...
\once \override TrillSpanner.script-priority = #-300
\appoggiatura{c8-3\startTrillSpan^\fngaLong} a2-1
c8\stopTrillSpan d4\fermata c8