Have you sequenced your vector and insert? If you have and you're sure you have the correct vector and insert I'd try a few things. It sounds like you're doing a double digestion, I suggest doing it in sequence instead and for at least 4h instead of 3. I'd also try running your digested vector in a gel and extracting the vector band to eliminate the 40bp fragment and avoid re-ligation. If you're doing your ligations at 4 degrees I suggest doing it overnight at room temperature, as long as your samples are DNase free. Id also advise to do some lambda ligation as a control to make sure your ligation is working.

Dear Aniket Banerjee i agree with several points from Mariana. The key points that can go wrong is that not both enzymes cut efficiently, the Ligase is not efficient, or (less likely) your transformation efficiency is low. When you say false colonies, are they the empty pET28B? The things to make sure are: A) is your vector cut by both enzymes? check that u are using a good buffer for both enzymes (see company webpages tools, e.g. Thermo double digest calculator), and add a bit more of the enzyme with less efficiency. You can make a control with no, 1, the other, and 2 enzymes and run on the gel together to double check that they both work. Cut and purify always from the gel. You can include dephosphorylation of the digested vector directly after digestion before running the gel to keep any remaining vector that is only cut by one enzyme from religating. B) is your insert cut well? Are you cutting out of a backbone and can see well that both ends are cut or are you digesting a PCR product? restriction sites close to the ends are less efficiently cut (eg. check here https://www.neb.com/en/tools-and-resources/usage-guidelines/cleavage-close-to-the-end-of-dna-fragments). Subcloning the PCR fragment first can help in that case. Also purify the digested insert via gel of course. For the Ligation, the concentrations should be verified by running an aliquot on gel (nanodrop especially low values are sometimes not so accurate). 2:1 or 3:1 is ok, more is not helpful i think. For Ligase u can also make a control with a singe enzyme digested not dephosphorylated vector. Finally, check that transformation efficiency is decent. Low efficiency makes it harder to get larger plasmids. Good luck.

@Marina Kaufmanner and @Daniela Liebsch, thank you for you answers. I have always ran the restricted digested products on agarose gel, and subsequently purified them. My nanodrop readings also seem to be okay, as I tend to get around 40-50ng/ul of DNA (both insert and vector, purified from agarose gel). So far, I have been ligating at 16°C for 16 hours.

Dear Aniket Banerjee that is great. I assume in the gel u see that the vector was well cut at least once (I don't know of u can see that both sides are cut, because the distance is very small, if you have another vector with an insert between bamhi and xhoi to cut out to see better that both sides are cut that could help?) and my question about the insert you want to clone, you also cut it from a vector and see both sites are cut? If you can see by the release of fragments that the cutting went well, it is likely the ligation step. Even if your concentration of fragment is ok i'ld still check it in a gel just to see that all is ok (no degradation etc). For ligation, I do routinely 4° over night and that always works for me, but 16° 16h is also ok or even much shorter at RT. There could be a problem with either your Ligase or the buffer. Sometimes the buffer gets old (the DTT and ATP i think are the critical things). We mostly have it in small aliquots and sometimes we add additional ATP to the ligation, u can try that. I would include some control (as mentioned above, just linearized plasmid cut with one enzyme + ligation) or something easy to check on gel like suggested by Marina. Hope it works!