It’s actually part of the equity so neither an asset nor a liability. I’ll try to explain it a bit more in detail. Every company has specific authorized capital. Let’s say for example, that company A has authorized paid capital of 100 shares (share class 1) with nominal value $1 each.
Normally, the shareholders would buy these shares and contribute $100 (100 * $1). That does not mean that they can not contribute more than $1 for each share.
So the amount that is paid in excess of the nominal value is the additional paid in capital. It is also called as share premium (actually share premium is what is most commonly called).
Using the above example, if the shareholders paid $200 instead of $100, the accounting treatment and the journals would be:
Debit Cash $200
Credit Share Capital $100
Credit Share Premium $100
Share premium can be sometimes included in the share capital account but IFRS (and 99% companies that follow US and UK GAAP) record them separately.