Why SERP API Google Scholar search does not filter by date?

Question

I am trying to use SERP API to make a call in Google Scholar. These are the test parameters that I am using:

params = {
        'api_key': 'x',  
          'search_type': 'scholar',
        #  'q': '"cloudberry pie"', # This is a search term with very few results (when you test the code you don't want to spend all your credits)
          'q': SearchKeywords,
          'lr': 'lang_en', # Only English results
          'scholar_include_citations': 'false', # don't include citations
          'scholar_year_min': '2023', 
          'scholar_year_max': '2023', 
          'hl': 'en', # Force Google to use the English UI when it returns results. We tried it without this parameter and this led to using a different language with every search, and interestingly to duplicate publications as well.
          'sort_by': 'relevance',
        }

Since SERP charges for each page of results and it costs a lot, I was thinking to sort by date and limit the number of results using these parameters:

params = {
        'api_key': 'x',  
          'search_type': 'scholar',
        #  'q': '"cloudberry pie"', # This is a search term with very few results (when you test the code you don't want to spend all your credits)
          'q': SearchKeywords,
          'lr': 'lang_en', # Only English results
          'scholar_include_citations': 'false', # don't include citations
          'scholar_year_min': '2023', 
          'scholar_year_max': '2023', 
          'hl': 'en', # Force Google to use the English UI when it returns results. We tried it without this parameter and this led to using a different language with every search, and interestingly to duplicate publications as well.
          'sort_by': 'date',
          'num': '10'
        }

But I get this error:

{
  "request_info":{
                  "success":false
                  "message":"Error whilst validating Search: 'num' parameter is not supported                       when 'search_type=scholar'."
                  }
   }

Do you have any suggestions on how to achieve this sorting by date and getting a predefined number of results?

I tried with these parameters:

params = {
        'api_key': 'x',  
          'search_type': 'scholar',
        #  'q': '"cloudberry pie"', # This is a search term with very few results (when you test the code you don't want to spend all your credits)
          'q': SearchKeywords,
          'lr': 'lang_en', # Only English results
          'scholar_include_citations': 'false', # don't include citations
          'scholar_year_min': '2023', 
          'scholar_year_max': '2023', 
          'hl': 'en', # Force Google to use the English UI when it returns results. We tried it without this parameter and this led to using a different language with every search, and interestingly to duplicate publications as well.
          'sort_by': 'date',
          'num': '10'
        }

But I got this error:

{
  "request_info":{
                  "success":false
                  "message":"Error whilst validating Search: 'num' parameter is not supported                       when 'search_type=scholar'."
                  }
   }

I would expect to get just the first 10 results sorted by date.