Not able to install 15.3 os in iphone 6s

Optimize the range of the mobile network, see this Apple article: If you see No Service or Searching on your iPhone or iPad

https://support.apple.com/en-us/HT201415

Check also the Wi-Fi network, see the following Apple articles:

Connect to Wi-Fi on your iPhone, iPad, or iPod touch

https://support.apple.com/en-us/HT204051

If your iPhone, iPad, or iPod touch won’t connect to a Wi-Fi network

https://support.apple.com/en-us/HT204051

Low Power Mode is On.

Charge the iPhone, Wait until the battery is fully charged (100%).

The Low Power Mode will turned off automatically.

Then you can perform the update.

You need about 6GB device storage, see this Apple articles below

If you need more space for an update on your iPhone, iPad, or iPod touch

https://support.apple.com/en-us/HT203097

How to check the storage on your iPhone, iPad and iPod touch

https://support.apple.com/en-gb/HT201656

Clear Other storage on your iPhone or iPad

https://support.apple.com/en-us/HT211686

What's the difference between device storage and iCloud storage?

https://support.apple.com/en-us/HT206504