Hi cmkabir,
We recommend that you try the steps in the link below since you're having an issue with charging your MagSafe Battery Pack.
How to use your MagSafe Battery Pack - Apple Support
To perform the recommended troubleshooting steps via the link above, complete the steps in the section titled "Charge your MagSafe Battery Pack and your iPhone."
If both your iPhone and MagSafe Battery Pack need to be charged, you can charge them at the same time. Plug the MagSafe Battery Pack into a power adapter and then attach your MagSafe Battery Pack to your iPhone. Using a 20W or higher power adapter, the MagSafe Battery Pack can charge your iPhone with up to 15W of charging power.
You can also charge both if you attach your MagSafe Battery Pack to your iPhone, then plug your iPhone into a power source. You might want to charge this way if you need to connect your iPhone to another device while charging, like if you're using wired CarPlay or transferring photos to a Mac.
If you charge your iPhone and MagSafe Battery Pack at the same time, your iPhone might charge to 80% or higher before your MagSafe Battery Pack begins charging.
We recommend the steps above because they will show you how to charge your MagSafe Battery Pack and your iPhone.
If you’re still experiencing the same issue, we recommend contacting Apple Support directly so that they can work with you to find a solution.
You can reach them by clicking here: Apple Support or calling the most local number in your region: Contact Apple for support and service - Apple Support
Thank you for participating in the Apple Support Communities.
Cheers!