$2 NLHE 6-max: Fold my gut shot whenever villain leads down on Turn?

Should I be calling the Turn bet right here? Can I have led down in the change? We missed my right in the turn and so I checked and villain led I was like 10:1 to hit that Q. Did I play this correctly out.. I think the money was 3:1 but? Trying to learn from you folks that are friendly. Many thanks. I am hoping i did so this right.

https://www.cardschat.com/replayer/5qTqua6

Stacks:
UTG – UTG ($2.71)
MP – MP ($2.18)
CO – CO ($0.00)
BTN – BTN ($0.71)
SB – SB ($3.49)
BB – Hero ($1.76)

Preflop: ($0.03, 6 players) Hero is BB with Kd 9d
1 fold, MP raises to $0.06, BTN raises to $0.10, 1 fold, Hero calls $0.08, MP calls $0.04

Flop: Jc Th 4h ($0.31, 4 players – MP: $2.08, CO: $0.00, BTN: $0.61, Hero: $1.66)
Hero bets $0.07, MP calls $0.07, BTN calls $0.07

Turn: 3s ($0.52, 4 players – MP: $2.01, CO: $0.00, BTN: $0.54, Hero: $1.59)
Hero checks, MP checks, BTN bets $0.26, 1 fold, MP calls $0.26

River: Qh ($1.04, 3 players – MP: $1.75, CO: $0.00, BTN: $0.28)
MP checks, BTN checks

Total Pot: $1.04
MP shows Jd Kh (a couple of Jacks [Jd Jc Kh Qh Th])
BTN programs Ts Ah (a couple of Tens [Ts Th Ah Qh Jc])

MP wins $0.99 from main pot

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