I lost my job about 7 months ago. Because of this, I have file a petition to modify my child support here in Florida, as that was a substantial change. My ex is now claiming that I lost my job as a direct result of an arrest that I had. I had a full time job that I was let go from in October of 2014, however at that time I also had a part time seasonal job that ended in April of 2015. I was arrested March of 2015 and am currently on probation and they also withheld adjudication. I have proof that I was let go from my full time job prior to the investigation that led to my arrest. He is claiming that because I was arrested that caused me to lose my job. Is there any way that I can defend myself on this? Everything I'm reading is kind of confusing. I have been trying to find a job, however everyone else is too. Any guidance would be helpful.

You have documentation with dates to verify your side of the issue. Simply present them before the judge (Or arbiter) at the hearing to rebutt his claims.

I'm not sure what unclean hands has to do with this. What motions has you ex filed? He can claim anything he wants, but he will be required to furnish proof. You just need to furnish your proof against his motions.

I'm not sure what unclean hands has to do with this. ...

Nothing really. The "unclean hands (https://en.wikipedia.org/wiki/Clean_hands)" doctrine is a defense properly used in equity (injunctions, etc.), not a child support action such as this. But, as OP freely admits, he is confused by all of this legal mumbo-jumbo. What we are trying to do here in the AMHD, as you know, is to help un-confuse OPs such as him.

In any event, OP's best course of action, as noted, is to clearly present his proof that her termination had nothing to do with being charged with a crime.

I would also note that in Florida (as in most if not all other states), law and equity have been merged for the greater part of a century, but (or perhaps as a result) Florida jurists and lawyers also seem to be somewhat confused about the distinctions between "law" and equity doctrines.

First even if you were put in jail, being put in jail is a reason to modify child support. Even if you lost the job due to a criminal activity, I am not sure that it would have any real difference on the modification.

But, you merely prove she is wrong. You show the date of arrest, (get a copy of the police report) and then show date of termination, (should have a termination letter from where you work )

... Even if you lost the job due to a criminal activity, I am not sure that it would have any real difference on the modification.
...

I agree, but I gathered from what OP wrote earlier that such is what the custodial parent is trying to argue. The argument would be that OP chose to commit a crime, as a result became unemployed voluntarily, and thus her income in her previous job should be attributed to her. It might be a good idea for OP to (in addition to making the factual proof we've already discussed) find case law to back her position.