AC adapters for charging mobile phones from an AC source are called wall mount mobile charger for mobile phones. mobile charger does not contain batteries. If you are travelling through flight with a cabin bag or hand bag better to keep charger with you, incase of flight delays or multi city flight booking or change of planes, with low mobile battery you can always charge your mobile phone with mobile charging port available at airports.
here are the links for getting Detailed baggage guidelines for AirIndia available at https://www.airindia.com/in/en/travel-information/baggage-guidelines.html
Detailed baggage guidelines for Indigo Airlines available at https://www.goindigo.in/baggage/dangerous-goods-policy.html and baggage information on https://www.goindigo.in/baggage.html
From these you will get a fair idea about things to be carried while travelling through flight