Try putting it into DFU mode and restoring it from iTunes. If that does not fix the issue then it would be a hardware problem and you would need to take it to an Apple store or an Authorized Apple Service Provider.

This happened with my iPad, the problem was my battery completely died while turned on and didn't give the iPad enough time to shut down fully,

So when you plug it in it charges but as soon as it gets to 1% or less it auto tries to turn on and boot up, but by the time it almost gets to the lock screen it uses the little bit of charge and dies again. And this will continue over and over.

The way to fix this is

Plug it in on charge
Once the apple logo appears hold home button and power button in until it resets

Then when the apple logo appears again press the buttons again

Keep repeating this over and over (my iPad took 100 resets)

Then finally when the apple logo appears let it boot as normal and it should make it to the lock screen

Then just leave to charge, I'm not saying this will work for you but it did for me

What version of iPhone do you have? What's the iOS version? Is it jailbroken?