Hi. The fee you pay is for the miners to confirm your transaction.
If the network is very busy, the transactions with lower fees will wait since the higher fees are preferred by the miners.
The smarter wallets try to help you and propose a fee. The wallets with all functionalities there will allow you to select a different fee than the proposed one, even down to 1 sat/byte.

So all you need is a good Android wallet. I use Mycelium, but I use it so rare I cannot tell if it's the best in town or "just another wallet". It allows, however even 1 sat/byte fee.