You may be innocent ~, but they won't care.
It sounds like you have a police-problem, not a money-problem. I'm glad I live in a country where I'm innocent until proven guilty.
All countries/central banks issue banknotes
with serial numbers for a reason... there is no exception.
This is a long-time international practice, so I'm surprised you've never heard it before:
https://www.reddit.com/r/explainlikeimfive/comments/3ou4h4/eli5_how_are_the_serial_numbers_on_banknotes/https://en.wikipedia.org/wiki/Bait_moneyBait money or bait bills are bills with known serial numbers, used by banks to aid the tracing of bank robbers.
The serial numbers are recorded by the bank either by making a copy or by listing in a log book. During a bank robbery, if a robber has taken the bait money, details of this can be passed on to the police. If the money is found in the possession of someone, or used to purchase goods, this can make it easier to find the suspect of the bank robbery.[1] Bait bills were used by investigators of the 1932 Lindbergh kidnapping in the United States.[2]
In the future it might get even worse:
https://www.eetimes.com/euro-bank-notes-to-embed-rfid-chips-by-2005/https://www.fleur-de-coin.com/eurocoins/banknote-rfidAs soon as that "tainted" banknote enters the banking system, you're fucked. They will freeze the money and the police will interrogate you where you got it from.
I have never heard of this happening before. Cashing into the bank is much rarer than cashing out, maybe that's why. Usually, you have more money in the bank than in cash.
Even if it happens, what do the police expect from me? Cash is untraceable. I have no damn clue where I sent or received a particular banknote. Any response I give to the source of the money cannot be verified.
I wouldn't say it's rare... many people (especially shops) who get paid in cash make ATM deposits on a daily basis. That's why they have more money in the bank (the money has to come from somewhere).