Mostly depends on the DNA you are transfecting with and if you have used any chemicals/procedures that induce double strand breaks. If you transfect with single stranded or linear DNA then there is a higher chance of genomic insertion. Double strand breaks in the host genome caused by improper freezing protocols or freeze thaw cycles or chemicals used to make the cells competent can increase the odds of genomic insertion assuming the cell is still viable. Both of your transfection methods should not induce double strand breaks unless you have some restriction enzymes contaminating your plasmid. If your plasmid expresses any transposases or CRISPR systems then that can cause genomic insertion.

The best method to test for genomic insertion is to perform a restriction digest using a common restriction site in your host genome that is not in your plasmid GOIs, ligate at a low dilution to circularize and then perform PCR outwards from the ends of your GOIs. If you find any unexpected band sizes you can then sequence them and map to the host genome.

Thank You sir Robert Adolf Brinzer

We are using piggybac gene delivery tool where we use piggbac DNA and our DNA construct with gene of interest in it. Does this piggybac DNA encodes for transposases which then takes out the gene of interest from our gene of interests and then inserts it into the host genome at AATT site? Is it correct?

Yes piggybac is a transposon based plasmid system. Check if you are using a binary plasmid variant or not since some versions have the transposase on a separate plasmid. I would not advise using that plasmid if you only want transient transfection.

Thank you for your valuable response sir. We have binary version with transposase encoding helper plasmid in it.

If you transfect without the helper plasmid then you will have transient transfection.