how to t-type splice power wires to add a new outlets?
The usual solution is not &quot;t-type connections&quot;. You normally can't do that inside walls. Assuming you don't have ~ 2 feet of slack in the wires, the way to do this is with two boxes a few feet apart. The key is that each box has to have several inches of wire inside the box. Hopefully you can do this without making three holes, but conceptually:
Note: You should actually cut all the holes at one time, otherwise you may &quot;lose&quot; the cable when you cut it. Also, be really, really sure, that power is off before you cut the cable, or you may be in for a shocking experience.

Hole # 1

Cut the cable.

Hole # 2 - at least a foot to the left of hole # 1.

Route the left section of the cut wires into a new box.
Add a new 3-foot section of cable and connect that as well (pigtail or in on one side, out on the other).

Hole # 3 - at least a foot to the right of hole # 1.

Route the right section of the cut wires into a new box.
Connect the new 3-foot section of cable as well (pigtail or in on one side, out on the other).
If having 3 receptacle boxes is OK then you could put a receptacle into hole # 1 as well, with one new section of cable from # 2 to # 1 and one from # 1 to # 3. If you don't like patching drywall, that may be less work than patching hole # 1.