When I was a child, I would always look forward to Saturday mornings, as that was the day I’d receive a dollar from my dad to put towards whatever toy I was hankering after at the time. In Italian, the word for pocket money or allowance is paghetta (feminine, plural: paghette).
Paghetta is the diminutive form of paga which means salary, pay or wages.
I miei genitori mi danno la paghetta ogni settimana.
My parents give me pocket money every week.
One possible (albeit far less common) synonym for paghetta is mancetta (the diminutive form of mancia = tip, gratuity).