Not sure what you mean by barbecue as in whether you mean barbecue, ribs, barbecue chicken etc or you mean barbecue sauce.
If you're asking about barbecue meat then you can keep the barbecue meat in the refrigerator for around 3 to 5 days before it goes bad.
As for barbecue sauce it can last for months in the refrigerator and can even be left out on the counter or in the pantry for months even after being opened before it goes bad.
If it's barbecue meat you want to keep longer than 5 days then you should freeze it instead of refrigerating it because frozen meats keep longer than refrigerated meats due to the cold freezing temps.