So this is a problem I've been having with the various DOS related Combat Sim games, not just TIE Fighter. The aspect ratio seems to have problems once I get into the cockpit. In the concourse everything is fine but once I take flight, the borders of the screen get cut off so the edges of the cockpit wont display as well as parts of the dialogue or information that would be said to me at the bottom. It's not a serious problem but, it's insanely distracting and annoying. I've played around with the DOSbox config program but nothing so far has actually affected this issue. Most annoying is that I'd screen cap for example but it displays just fine. Hoping someone might know whats going on here.

Have you tried setting the fullscreen resolution the same as your desktop?
Are you using a widescreen monitor?

My monitor is a 1776x1000. I didn't see a screen resolution in that size in the DOSbox option settings.

You are using a launcher?
Edit the configuration file directly using notepad (there should be two, the longer one is the one with the options for resolution) you should be able to type in your resolution.

This is an example from my Tie Fighter file:

# This is the configurationfile for DOSBox 0.74. (Please use the latest version of DOSBox)
# Lines starting with a # are commentlines and are ignored by DOSBox.
# They are used to (briefly) document the effect of each option.

[sdl]
# fullscreen: Start dosbox directly in fullscreen. (Press ALT-Enter to go back)
# fulldouble: Use double buffering in fullscreen. It can reduce screen flickering, but it can also result in a slow DOSBox.
# fullresolution: What resolution to use for fullscreen: original or fixed size (e.g. 1024x768).
# Using your monitor's native resolution with aspect=true might give the best results.
# If you end up with small window on a large screen, try an output different from surface.
# windowresolution: Scale the window to this size IF the output device supports hardware scaling.
# (output=surface does not!)
# output: What video system to use for output.
# Possible values: surface, overlay, opengl, openglnb, ddraw.
# autolock: Mouse will automatically lock, if you click on the screen. (Press CTRL-F10 to unlock)
# sensitivity: Mouse sensitivity.
# waitonerror: Wait before closing the console if dosbox has an error.
# priority: Priority levels for dosbox. Second entry behind the comma is for when dosbox is not focused/minimized.
# pause is only valid for the second entry.
# Possible values: lowest, lower, normal, higher, highest, pause.
# mapperfile: File used to load/save the key/event mappings from. Resetmapper only works with the defaul value.
# usescancodes: Avoid usage of symkeys, might not work on all operating systems.

fullscreen=True
fulldouble=True
fullresolution=1920x1080
windowresolution=original
output=openglnb
autolock=true
sensitivity=250
waitonerror=true
priority=higher,normal
mapperfile=mapper-0.74.map
usescancodes=true

[dosbox]
# language: Select another language file.
# machine: The type of machine tries to emulate.
# Possible values: hercules, cga, tandy, pcjr, ega, vgaonly, svga_s3, svga_et3000, svga_et4000, svga_paradise, vesa_nolfb, vesa_oldvbe.
# captures: Directory where things like wave, midi, screenshot get captured.
# memsize: Amount of memory DOSBox has in megabytes.
# This value is best left at its default to avoid problems with some games,
# though few games might require a higher value.
# There is generally no speed advantage when raising this value.

language=
machine=svga_s3
captures=capture
memsize=32

[render]
# frameskip: How many frames DOSBox skips before drawing one.
# aspect: Do aspect correction, if your output method doesn't support scaling this can slow things down!.
# scaler: Scaler used to enlarge/enhance low resolution modes.
# If 'forced' is appended, then the scaler will be used even if the result might not be desired.
# Possible values: none, normal2x, normal3x, advmame2x, advmame3x, advinterp2x, advinterp3x, hq2x, hq3x, 2xsai, super2xsai, supereagle, tv2x, tv3x, rgb2x, rgb3x, scan2x, scan3x.

frameskip=0
aspect=true
scaler=none

Perhaps it was the text file with all the text amassed horizontally, if you used the dosbox configurator GOG provides it might have messed up the file formatting however it should be still functional only finding the values might to modify might be more annoying that way.

Use Notepad++, Wordpad, etc. Notepad doesn't like *nix line endings.