To create an offer on an existing service, i.e. lower the price for a limited time, go to your Appointedd calendar screen:
Hover over the Setup tab and click on Manage services
Click the pencil icon next to the service you want to be discounted
Under Type of service > Duration and price, click the three dots next to the appropriate duration
Adjust duration if needed
Select the appropriate Price Type and enter the new price in the Original and Discounted price boxes
Click Save service
The new price will now appear on your Booking Page and booking widget. The original price will be struck out beside the new price so that customers can see the saving.