An electrician put in two new outlets in the basement that are wired together and go to a new breaker he put in the main panel. He use GFCI outlets for both boxes that are on the same line. I want to add one more outlet and come out from the second box in line that he installed and I will purchase another GFCI outlet as seeing how for each he used GFI ones so I see how he installed them.
He has the romex coming from the breaker box and that is wired to the 1st outlet. : White is pushed into slot near bottom on the top push in slot (of bottom) and black is on right side top push in slot (of bottom connection). Now this is with the outlet with the round hole on the bottom. I've seen some electricians install the 3 prong with the round hole on the top.
Then from that first outlet a new romex line comes out of that GFI outlet and goes to the second outlet and this is wired: White to bottom push in on bottom left side as you look at it in the outlet box and the black to bottom push in on the bottom right of gfi. This runs to the second GFI outlet (Cooper) and the white goes to the top left push in connector with the push in connection located on the bottom of the outlets and the black goes to the right side bottom and is pushed into the bottom of the 2 push in connectors and nothing goes into the top of this bottom push in.
Naturally the grounds are twisted in the first box and connected to the outlet ground and the second outlet has the one ground to the ground outlet.
If I come off this second outlet to add another outlet and use a GFI even though they are more expensive, can I put the new romex in the open push in slots to come out of this outlet so that would be new outlet black to top push in slot located on bottom of outlet and white in bottom push in slot located on bottom of outlet. Then I’d run this to new outlet and does it matter if I put the black and white wires into the top or bottom push in slots on this new outlet?
Not of the top connectors on any of the outlets are used and the bottoms of the outlets have a top and bottom push in slot.
Hope I’ve explained this correctly. Thanks.

GFI's Have a "LINE"(Top), and a "LOAD"(Bottom). If the power goes to first gfi line, then load to second gfi, Then if firs GFI trips, everything else will trip.
IF at first receptacle you wire both blacks together and to line hot, and both whites together, and to line neutral, then, If First GFI Trips, others remain on, and protected.

Response was not the answer I was looking for. I need to know if I have to move the current second and last online gfi in order to run a new wire to make a 3rd outlet off this connection and the third outlet with now be last online.

Yes you can add to it,
You could have 3 last online? If you run to a new receptacle, use a regular, not GFI, it will already be protected, provided it is connected to load side, of gfi feeding it. Sorry if still not answered.