Meaning
To fix on someone and harass or torment them persistently — to single a person out for continual picking, teasing, or trouble. 'Him tek set pon mi' means he keeps picking on me and won't let up, and to have someone 'tek set' on you is to be their steady target, pursued and needled without relief. The phrase names a dogged, deliberate campaign of bother against one person, and it carries the real weariness and grievance of being the one constantly picked on.
Examples
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Di bigger bwoy dem tek set pon di likkle one.
The bigger boys kept picking on the little one.
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Since mi seh no, she tek set pon mi.
Since I said no, she's been on my case constantly.
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Nuh badda tek set pon mi today, mi nuh inna it.
Don't keep harassing me today, I'm not in the mood.
Origin
From 'tek' (take) plus 'set' (to settle/fix upon) — to set yourself persistently against a person.
How it’s used
Almost always 'tek set pon [someone]' — to persistently harass or pick on them.