MySql query with OR parameter
You need to apply proper parenthesis ( ). You need to apply parenthesis for the condition (task_assigner = 31 OR task_assigned_to = 31), so the task_status IN ('0', '3') and the task_assigner both conditions will satisfy.

The working query will be:

SELECT task_name, task_id, SUBSTR(task_text, 1, 20) AS task_text,
       task_project_id, task_status
FROM projectboard_tasks
WHERE task_status IN ('0', '3')
    AND (task_assigner = 31 OR task_assigned_to = 31)