“Dominance and submission” or “dom/sub” does not apply to “sub” sandwiches, but there are jokes.
   
“Meatball dom / meatball sub” was posted on Twitter by Cousin Cole on December 28, 2012. “The existence of a meatball sub implies the existence of a meatball dom” was posted on Twitter by Lizzy Pitts on October 12, 2019.
   
“The existence of the meatball sub implies that there also exists a meatball dom” was posted on Twitter by linds on April 21, 2020, and the tweet went viral. “The existence of the meatball sub implies that there is a meatball Dom” was posted on Reddit—Oneliners on September 18, 2020.
 
“I want to open a BDSM-themed sandwich shop called Dom’s Subs” is a related joke.
   
       
Wikipedia: Dominance and submission
Dominance and submission (also called D/s) is a set of behaviours, customs, and rituals involving the submission of one person to another in an erotic episode or lifestyle. It is a subset of BDSM. This form of sexual contact and pleasure has been shown to please a minority of people.
       
Twitter
Cousin Cole
@COUSINCOLE
Replying to @Jlamarwashere
@Jlamarwashere meatball dom / meatball sub
8:10 AM · Dec 28, 2012·Echofon
   
Twitter
Brook
@quadspawning
“i asked for a meatball dom not a meatball sub” (crowd cheers and the Sandwich artists at subway start breaking dance with me)
6:02 PM · Oct 28, 2013·Twitter Web Client
   
Twitter
la pumpkin
@lapumpkinmusic
@lapumpkinmusic meatball sub? im really more of a meatball dom.
8:09 PM · Apr 4, 2014·Twitter Web Client
     
Twitter
red onion stan
@jawbutch
Note to self: flesh out meatball sub/meatball dom joke.
9:59 PM · Nov 30, 2016·Twitter for iPhone
   
Twitter
daniel day louis xiii
@egg_dog
[subway ]
Me: marinara plz
Sandwich genius: meatball sub?
Me: i’m more of a meatball dom.
8:21 PM · Jan 20, 2017·Twitter for Android
     
Twitter
ryu gosling
@bbbeloveddd
meatball sub for lunch
meatball dom for dinner
1:36 PM · Nov 17, 2017·Twitter for iPhone
   
Twitter
radical goose
@___MakutaMatata
Meatball sub? weak. i want a meatball dom
11:22 AM · Mar 1, 2019·Twitter for Android
   
Twitter
yamaguchi mane
@nurvuss
Meatball sub seeking meatball dom
1:25 PM · Apr 14, 2019·Twitter Web App
   
Twitter
Lizzy Pitts
@LIZardz_
The existence of a meatball sub implies the existence of a meatball dom
9:18 PM · Oct 12, 2019·Twitter for iPhone
   
Twitter
Nick Gamb(l)er
@YABOYNICKYG
The existence of a meatball sub implies the existence of a, much more aggressive, meatball dom.
6:57 PM · Jan 1, 2020·Twitter Web App
   
Twitter
unshaken
@AutoYotsuba
the fact that there is a sandwich called a “meatball sub” suggests that there is a sandwich known as the “meatball dom”
Quote Tweet
ⓈⒺⒶⓃⒾⒺ
@Floridian_Lad
· Feb 7
Meatball sub
12:02 PM · Feb 7, 2020·Twitter Web App
   
Twitter
Queen Glizzybeth III
@TreestarOO
The existence of the Meatball Sub
suggests the existence of a
Meatball Dom
1:18 PM · Mar 13, 2020·Twitter for iPhone
   
Twitter
Danny Neary
@itsdannyneary
The meatball sub implies the existence of a meatball dom.
2:25 AM · Apr 6, 2020·Twitter Web App
 
Twitter
linds
@Lwowwy
The existence of the meatball sub implies that there also exists a meatball dom
10:50 AM · Apr 21, 2020·Twitter for iPhone
     
exclaim!
This Funny Week in Funny Tweets: April 24, 2020
By Vish Khanna
Published Apr 25, 2020
(...)
April 21
linds
@Lwowwy
The existence of the meatball sub implies that there also exists a meatball dom
10:50 AM · Apr 21, 2020
 
Reddit—Oneliners 
Posted by u/jtrier1 September 18, 2020
The existence of the meatball sub implies that there is a meatball Dom