I guess you first have to find out with what he is min-raising. But let's assume the player is unknown to you. The hand below is an example of one of them. Would you have attacked and raised on the flop? My two pair was not that strong but neither was his bet. While there was a few possible draws on the turn I believed I had the best hand because it was checked to me. However, river card could have completed a straight and villain could easily have had one, so I checked the river.
PokerStars Pot-Limit Omaha High, $0.02 BB (8 handed) from (Format: FlopTurnRiver)
MP1 ($7.32)
MP2 ($3.14)
Hero ($1.61)
Button ($2.71)
SB ($0.98)
BB ($3.67)
UTG ($3.13)
UTG+1 ($5.59)
Preflop: Hero is CO with J




UTG calls $0.02, UTG+1 calls $0.02, MP1 calls $0.02, MP2 calls $0.02, Hero calls $0.02, 1 fold, SB completes, BB checks.
Flop: ($0.14) J



SB checks, BB checks, UTG checks, UTG+1 checks, MP1 checks, MP2 bets $0.04, Hero calls $0.04, SB folds, BB folds, UTG calls $0.04, UTG+1 folds, MP1 calls $0.04.
Turn: ($0.30) T

UTG checks, MP1 checks, MP2 checks, Hero bets $0.3, UTG folds, MP1 folds, MP2 calls $0.30.
River: ($0.90) Q

MP2 checks, Hero checks.
Final Pot: $0.90
Results in white below:
Outcome: MP2 wins $0.90.