[talanum1]

"Momentum charge" is the charge necessary for a particle to be able to carry momentum. It's like an electric charge. A photon has to have momentum charge to be able to follow a curved path in curved spacetime.

[Bored chemist]

"Momentum charge" is the charge necessary for a particle to be able to carry momentum

No
"Momentum charge" is something you made up.
The thing that allows particles to carry momentum is called "mass".

[talanum1]

The thing that allows particles to carry momentum is called "mass".

Yes, but a photon is massless, yet it must have something like mass. I chose "momentum charge" as a reasonable name.

So, I take it you don't have a better idea.

[Bored chemist]

yet it must have something like mass.

Yes... it has...  mass.
Confusingly, it is also massless.

No need to make up names.

[Kryptid]

"Momentum charge" is the charge necessary for a particle to be able to carry momentum.

Please provide evidence that a "charge" is necessary in order for an object to carry momentum.

yet it must have something like mass.

That "something" is called energy. E=mc².