The premium on common stock is the difference between the par value of a share of stock and the price at which a business sells the share to investors. Par value is the face value printed on a stock certificate; it is usually quite small, with $0.01 per share being a common amount. For example, if ABC Company sells a share of common stock to an investor for $10, and the stock has a par value of $0.01, then the premium on common stock is $9.99.
This premium is rarely recorded in an account having that name. Instead, it is more commonly recorded in an account called Paid-In Capital In Excess of Par Value. It may also be recorded in an account called Additional Paid-In Capital. The account appears in the shareholders' equity section of the balance sheet. It does not appear in the income statement.
When shares are traded between investors in the after-market (such as on a stock exchange), there is no impact on the issuing entity, since it is not participating in the trades.