My iPhone 5c shows wrong time

I have a iphone 5c using it more than 2 years.

One day the lcd crashed, so I bought a new one and replaced it by myself.

It had been off for a month until I received the new lcd.

After the replacement, I found it showed wrong time.

I tried many things, including restore, complete restore after DFU reset, changing settings of location, wifi, modem...etc with vain.

- When I set "Set Automatically" to off, I could set the time.

But every time I set, after some time, the time ran slow and showed wrong time.

Interestingly, when I set Auto-Lock to Never, then the time runs O.K, until I put the phone into sleep by pressing sleep button.

- When I set "Set Automatically" to on, I found a strange thing.

After 25 seconds it goes to "No Service", and come back to service.

It looks like the modem is restarting.

I do not have much understanding on iOS 10.

Can anyone comment on why this thing happens logically?