iPhone will only recognize certain charger

Hello Frantastic13,

You've walked through great step to help isolate the issue to certain chargers, and knowing the iPhone charges after restarting greatly helps with working towards a solution.

In addition to those steps, have you completing the steps listed below? If not, these steps are specific to resolving charging related issues with iPhone. You can also find these steps outlined in the following article.

1. "Check your charging cable and USB adapter for signs of damage, like breakage or bent prongs. Don't use damaged accessories.
2. Use a wall power outlet and check for firm connections between your charging cable, USB wall adapter, and wall outlet or AC power cable, or try a different outlet. 
3. Remove any debris from the charging port on the bottom of your device, then firmly plug your charging cable into your device. If the charging port is damaged, your device probably needs service.
4. Let your device charge for a half hour.
5. If your device is still unresponsive, force restart your device: 

• iPhone 8 or later and iPhone SE (2nd generation): Press and quickly release the volume up button. Press and quickly release the volume down button. Press and hold the side button until the Apple logo appears.
• iPhone 7, iPhone 7 Plus, and iPod touch (7th generation): Press and hold both the side (or top) button and the volume down button until the Apple logo appears. 
• iPhone 6s or earlier, iPhone SE (1st generation), and iPod touch (6th generation) or earlier: Press and hold both the side (or top) button and the Home button until the Apple logo appears.

6.Let your device charge for another half hour.

7.If your device still won't power on or charge, take your device, charging cable, and charging adapter to an Apple Store or Apple Authorized Service Provider for evaluation. You can also contact Apple Support."

If your iPhone or iPod touch won't charge - Apple Support

Let us know how that goes!