Steroid injection in the beard for hair growth can cause side effects, like stretch marks or any other ones?

Your questions is troubling because steroid injections do not usually grow beard hair (or any hair).  There are side effects associated with steroid injections (as with any medications).  However, stretch marks is not usually one of them.  

Steroid injections are generally quite safe, but yes, can have side effects. Injection of a small area is less likely to have side effects compared to injection of a large area. Furthermore, injection of a large area once every 3-4 months is less likely to have side effects compared to injection of a large area every month. Thinning of the skin, atrophy (dimpling of the skin), redness dilated blood vessels, are local effects. As you've pointed out there can be effects related to absorption of the medication - but it's rare and more likely to occur with higher doses, more frequent injections and larger areas covered. Be sure to speak to your doctor about the chances for you to experience negative effects.