I want to add a outlet outside but can I put a plug in adapter instead of tapping in into an existing outlet.
In general, Yes. There are a few things to be aware of.
Note also that I am speaking of the rules in Canada - USA is similar but there are some differences.
1) The Romex must be protected from physical damage.
2) It is illegal to run extension-cord wire through a wall. It is legal (and normal) to run Romex within or through a wall.
3) Be sure that you get the wire colors correct. Black is Hot and goes to the Brass-colored terminal on both the plug and receptacle. White is Neutral and goes to the Silver-colored terminal at both ends. The bare wire is Ground and goes to the terminals colored Green.
4) Because the receptacle is outside, be sure that there is a GFCI in the circuit somewhere. That can be either inside the building or installed in the outdoor receptacle box.
Absolutely not. You cannot just have Romex (in-wall wire) pop out a hole in the wall and loop around to put a plug on it. You cannot use Romex in a situation where flexing it would be involved, because it is solid-core wire and is extremely brittle. You cannot put a plug on solid-core wire because no plug made is rated for solid-core wire. You cannot be in a location such as a wall where it might be subject to damage - you cannot rely on the occupants being careful. Romex cannot swing away from the wall to enter the plug. You can't make an exception just because you don't know how else to do it.
Building cable (NM, UF, etc.) goes inside walls. Cordage (SJOOW, etc.) go outside walls and can go in places they are subject to flexing or disturbance. Cordage is entirely stranded wire, and fine-stranded not like THHN, that's why plugs aren't rated for solid wire. However cordage is not a legal use in this case. There's a way to work around that, though.
Here, you install a "surface conduit starter box" in front of the outlet you want to tap. Then you extend off that box with surface conduit, to the point where you want to send the cable through the wall. (which doesn't have to be far). Then, you fit a surface conduit junction box there, and at that point make the bend into the wall.
If you don't want a blank junction box with seemingly no purpose there, then fit a receptacle in that location. If you use a deeper box, you can even fit a GFCI receptacle - that way your required outdoor GFCI protection is in the dry, warm indoors where it will last 30 years instead of outside where it will last 3.
NM (Romex) or UF cable is legal in this situation. It is legal inside the walls, and it is legal in surface conduit. NM cable is not legal outside where the junction box will be subject to wet conditions.
If you want, you can fit the standard outlet outside, then connect that through the walls to a junction box on an inside wall. Inside that junction box, you fit an inlet. This is a "reverse socket" - with prongs instead of slots. Then, you use a short extension cord to connect the inlet to the nearby outlet. That extension cord is made of cordage, of course.
You must use an inlet because this cord must be plausibly removable. If you create a pendant, i.e. a hardwired bit of cord from the inlet box to the nearby outlet, then you violate NEC 400.8 and 400.7, which list uses permitted and not permitted for cordage.
Remember all outdoor outlets must be in a zone of the circuit protected by GFCI. The no-brainer way to do that is fit an outdoor rated ($$) GFCI receptacle outdoors. However, the smarter way is to add a GFCI device elsewhere in the circuit that is upline from your outdoor location, preferably somewhere indoors. This may be a problem for the inlet/extension cord approach, as nothing would stop you from plugging the extension cord into a non-GFCI-protected outlet.
You should connect the plug to romex and the romex to the fuse box, or connect the romex to another romex that powers outlets. (make this connection behind an existing outlet)
If you connect to existing romex you must use the same size romex. If you connect the the fuse box you must use romex of size apropriate for the fuse fitted.