An issue will appear on the board if the board selects for it.
Your question suggests that your "tasks" are sub-tasks, which will be selected by the board if their parent issue is selected. They will then appear inside their parent story because they are a part of it.
Ok, so your board is not selecting for tasks. You'll need to amend the filter so that it includes issue-level tasks as well as stories.
But, you say you want tasks to appear in the story and also "not a sub-task". You need to make up your mind whether you want tasks to be sub-tasks or not. They can't be both.
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