Old Roman Silver Or Something Else?

Looks like a cast replica to me with fake toning meant to look like tarnish, with frothing bubbles from the casting process at the feet of Spes and an attack by a Dremel on the obverse, obliterating the lettering in front of Trajan's face.

Just my take. Let's see what the experts say..

I agree with echizento,
nevertheless,
if you suspect that it may be fake have a look at those edge splits, looking for signs of tensile metal distress.
A cast coin cannot reproduce stress flan cracks - the inside of the 'split' has smooth surfaces inside the 'split'.

If you think that the black stuff on the surface of the coin is not sulfide / oxide staining, give the coin an acetone soak and any black waxy substance will be easily removed.
Have a look at the edge of the coin for evidence of a circumferential edge mold casting join, or evidence of tooling to remove it.

I note what looks to be verdigris below the feet of Spes, and
evidence of what appears to be accidental tooling in front of Trajan's neck, but they could just be scratches.

A fouree seems likely. Good call!
OP FYI a fouree is a contemporary counterfeit. Those have value. People collect them, and they often have the same style as the coins they are meant to emulate. In this case Trajan's head and the lettering look pretty good. But they are minted using non-precious metals, or are plated.
Regardless you may have a mystery on your hands...

I would say genuine (not always certain from just a photo), but a pic of the edge would help. Could be a fouree, but I see no other signs other than the green verdigris. I did have coin with similar green deposits and a some soaks in lemon juice and distilled water removed most of it. Note: this process will also remove most (if not all) of the toning and other deposits.