Here is a simple demo for your usecase.
First , im using a jsonPlaceHolder data check this API:
https://jsonplaceholder.typicode.com/users
second , i tried to do the following in Azure Data Factory:
- Created a webActivity to call the api(Its a simple GET request - please check the response).
- created a set variable activity to save and parse data to be used later.
- filtered data according to my condition

WebActivity :
Under settings, added the jsonPlaceHolder url and GET method, in headers : Content-Type : application/json.
SetVariable:
Under Variables , Name : data , Value : @json(activity('TestWebActivity').output.Response)
Filter Activity:
Under Settings , items : @variables('data') , condition : @startswith(item().username,'B')
Explanation:
here i set the variable name in set activity to "data", so now in variables
you can use data anywhere in your pipeline,
in Filter activity , i set the data array in "items" and basically each json in the array is reffered as "item()" , so in order to filter the json array based on a value , in condition you can select the key : items().keyName ..
in order to save your data to Blob storage , add a Copy activity after the filter and link the blob storage as a sink..