To get points per quarter with livestream API you need to follow instructions in documentation http://developer.geniussports.com/warehouse/livestream/read/index_basketball.html#Read_anchor and use types=bxa or types=bxt
bxa - boxscore - Statistics for teams and players for the match as well as statistics for players and teams broken down by period.
bxt - boxscore - Statistics for teams and players for the match as well as statistics for teams broken down by period.
API call example: https://live.test.wh.geniussports.com/v2/basketball/read/matchid?ak=you_api _key&types=bxa
change matchid with your matchid
change you_api _key with your api key