Meaning
To perch, prop, or rest something (or yourself) temporarily and none too securely — to balance in a spot, lean against, or squeeze in for a short while. To 'kotch' somewhere is to stay briefly or crash for the night without a proper place of your own.
Examples
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Mi just a kotch pon di chair edge fi a minute.
I'm just perched on the edge of the chair for a minute.
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Can mi kotch a yuh place till mi find somewhere?
Can I crash at your place until I find somewhere?
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Kotch di bag up pon di shelf deh.
Prop the bag up on that shelf.
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Mi jus a cotch yah fi a few day.
I'm just staying here for a few days.
Implies temporary, informal lodging rather than living there.
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Cotch di board pon di wall.
Prop the board against the wall.
Physical sense of resting one thing on another.
Origin
Possibly from 'scotch' (to prop or wedge); in Patois 'kotch' means to perch, prop, or lodge temporarily and precariously.
How it’s used
Implies temporariness and insecurity — a perch, not a settled place. Also 'kotch up'.