Petty Cash

In a business environment, the ubiquitous term for the pool of money, typically managed by a secretary or office manager, that one might spend on incidentals without having to fill an expense report, is Petty Cash.

I've also heard it used in non-business settings, but not as frequently referring to a pool of money, but more typically as an adjective describing the amount of money as being petty or trivial.

Example:

Yeah, Kobe is amazing. He bought that new whip with petty cash.

The OP's situation

That being said, in the example you provided, I believe petty cash would be a perfect fit. Imagine your Father saying:

Here Dear, put this with the petty cash.

or

Here Dear, add this to the petty cash.

Reference

From Merriam-Webster:

petty cash noun
Definition of petty cash
: cash kept on hand for payment of minor items