Hi Vamsi Madhav ,
Thankyou for using Microsoft Q&A platform and thanks for posting your question here.
As I understand your issue, you are getting an error: "Rest call failed with client error, status code 429" when you are copying the data from REST API to Synapse DB using copy activity.
To achieve this , your API should return the response in such a way that it contains some properties which describes the next range of request you want to fetch.
For example : If you take a look at this sample URL https://reqres.in/api/users?Page=1
, it contains the page number value and the API response gives the properties like total_pages which describes the total number of pages in the API , using which we can loop until the last page i.e. 2 in this case. Checkout this video to see implementation of the same: Copy data from REST API which sends response in Pages using Azure data factory
Similary , you need to check with your source API client/ admin team to help you get the properties that provides the range to iterate through the set of rows and read the data.
Additonal resources: https://learn.microsoft.com/en-us/azure/azure-resource-manager/management/request-limits-and-throttling#error-code
As stated in the above document , properties like 'Retry-After' can specify the number of seconds your application should wait , or 'x-ratelimit-remaining' can determine the remaining number of requests allowed. However, you need to check if it is supported in the API you are using or not.
Hope it helps.