Is this a fallacy? Who you are accusing always need a motive.

P1: X presents Y evidence.

P2: Y evidence on the associated party doesn't have any motive.

C: X is false because we don't know how it may benefit them.

Example: the prosecution finds evidence of the fingerprints of the accused on the gun that killed the victim, the defense says there's no motive or benefit for the accused that killed the victim therefore it couldn't be him.

I know of no specific fallacy that addresses lack of motive, perhaps because of its specific legal usage. This would fall under the generic non sequitur .

P1) Evidence Y suggests party A did a deed

P2) Party A has no motive

C) Party A is not guilty

Well, this is contingent on the veracity of P2. Does the person really have no motive? Was a motive necessary (e.g. is it a manslaughter case?) It would also help to look at P1 again to see if the evidence really does suggest something (e.g. it suggests this person did handle the gun...but are there any other fingerprints on there? What else do we know about the case - for instance, if the shooting happened at 9am, but the accused is only recorded as arriving at the crime scene at 10.30am, does it make sense to argue they were responsible?)

It's not a convincing argument - yet - because of the unsupported premise P2 - but it is defensible reasoning. 

There seems to be a hidden and unstated premise at play here -- something linking in some way (a) commission of a crime and (b) motive.  

As I understand the scenario, there is (some unknown quantity of) evidence to suggest that the accused committed a crime; at the same time, there is a lack of any (obvious) motive for the person committing the crime.  The premise that I see as missing (and that I see being central to the argument) is the assumption that a motive is necessary whenever there is a crime.

As written, the argument seems to be:

• this piece (or these pieces) of evidence suggest that the accused committed the crime
• there is no obvious reason for the accused to have committed the crime
• therefore, the accused didn't commit the crime.

There would be a logical flow to the argument if it were re-written as:

• this piece (or these pieces) of evidence suggest that the accused committed the crime
• there is no obvious reason for the accused to have committed the crime
• (a motive is required for a crime to be committed)
• therefore, the accused didn't commit the crime.

However, I suspect that many might not accept the now-stated third assumption as being true, rendering the conclusion suspect.

We deem the evidence incontrovertible for purposes here: Fingerprints were on the gun that killed the deceased.

On TV, we hear a lot about “means, motive, and opportunity.” While this is great when trying to convince a jury of guilt in a criminal proceeding, it is only an investigative tool.  A motive is not an element of the event here (death caused by gun, which — from what we know, could have been self-inflicted). A court should not convict merely on these three famous elements, but must find proof beyond a reasonable doubt of each element of a particular crime. 

At best, this is a feeble argument, as we can see by noting the implicit premise required to link the stated premise with the conclusion.
     
Beyond all that, he who proposes the proposition (implicit in this case that the defendant killed the decedent), bears the burden of proof. This is true in law (well, it is supposed to be), and epistemology. 

Fingerprints on the gun prove only that there are fingerprints on the gun. All else, under the fact situation set forth, is speculation. Perhaps we should call it the Fallacy of Speculative Evidence.