Hi All, can anyone suggest the ways of add a discount item by using extensibility API with out using promocode?

Fixed or variable discount amount?

variable discount

You're unlikely to be able to do this for the reasons mentioned in other recent threads, ie. price manipulation on the front end is unlikely to ever happen. You'd need to set up a discount item, add it on the front end, set the price in the back end with the scriptable cart - and possibly manipulate the front end view the user sees to fake the discount before order submission if you get any anomalies.

i understand that, but SC/SCA is not allowing to add discount item by the extensibility API

Just tested and get the "Discount line can only be added by promotion code" message. You'll have to use scripted cart in that case.