Investigate just using draft orders then marking paid when paid in full and either keeping order notes, or splitting into a new draft order with the amount remaining.
I'm pretty sure outside of India payment gates probably not going to find a gateway that does partial with cash because then how do they ensure their fees are being paid. If you are india check the shopify app store
It's either that or run your own business credit card dedicated for that purpose through the gateway.
Though before running your own card make sure you contact all involved services to see if that's okay and read ALL your terms and agreements as there's bound to be combinations where your not supposed to do that.