Custom group in characters viewer
The easiest way is to use each of the gitmoji emoji a bunch of times and then they will be in your frequently used list in the Emoji &amp; Symbols picker.

The categories/groups are defined by Unicode as ranges of the character set. I am not aware that it is possible to define your own. There are no clues in CharacterPicker.framework.

You could also setup keyboard text replacements so you can type :apple: and it will be automatically replaced with . I use Alfred to do this, but you could use System Preferences > Keyboard > Text to do it.

You could also try Dash, a document viewer/browser, that can be configured to show a Gitmoji cheat sheet. I have assigned a custom keyboard shortcut for Dash to appear.