I’ve created this variant suddenly. It’s played like international draughts, but on 12x12 board, with 2 free central ranks (30 pieces per army), but if piece takes, it can land on the next square behind captured one as well as on second square behind it (you take and land 1 or 2 squares after).

Is that ever possible)?

@Rechefiltr_is_Fire This is already known as CANADIAN draughts which is a native game to French speaking communities of Canada. They have own association: http://dames.quebecjeux.org/ .
International rules make Canadian draughts slow and less enjoyable in comparison to 10x10 or 8x8 boards, but 12x12 board is very good for playing under Frisian, South-German, Thai, Argentinian rules. You might explore this board by a program which allows to play established variants and to create own variants by combining known rules: hwiegman.home.xs4all.nl/alfacheckers12.html .

Anyway, is there a possible way to invent a variant with capturing pieces landing 1 (as usual) or 2 squares after taken piece?

@Rechefiltr_is_Fire This idea of capturing pieces by landing is not a novelty.
Because in any variant draughts is supposed to be a game where capturing of multiple pieces is distinctive feature, the capturing by landing must follow some particular rules.
Famous chess and draughts historian David Sargin in his book on chess and draughts games (in Russian, Древность игръ в шашки и шахматы, see wikipage ru.wikipedia.org/wiki/%D0%94%D1%80%D0%B5%D0%B2%D0%BD%D0%BE%D1%81%D1%82%D1%8C_%D0%B8%D0%B3%D1%80_%D0%B2_%D1%88%D0%B0%D1%88%D0%BA%D0%B8_%D0%B8_%D1%88%D0%B0%D1%85%D0%BC%D0%B0%D1%82%D1%8B ) describes North American draughts which are played under English rules, but with exception of king capturing move.
Unlike simple draughtsman, North American king must capture any piece or any sequence of pieces by LANDING, under condition that in the direction of capturing line there should be a vacant square behind a piece which is to be captured.
To be simple, this capturing rule:
a) enables multiple capturing;
b) does not turn king into vacuum cleaner (and those who play Turkish draughts may understand what lies behind this metaphoric expression);
c) excludes capturing of enemy pieces which are located in edge squares, because there are no vacant squares behind it;
d) excludes capturing of enemy pieces which are protected by any enemy piece or which are blocked by some own piece.
In the same book David Sargin suggests a WHOLE NEW CLASS of draughts games based on this capturing rule, and he proposes to mix traditional rules (for example, Italian, Polish / International etc.) with that king rule. As well, he admitted that even simple draughtsman can execute capturing by landing under same condition.
Personally, I like his idea, and I can only regret that his idea had not find an echo among Russian players.
However, the good news is that you can try this variant online.
North American draughts can be played at glukkazan.github.io/checkers/north-american-checkers.htm .
There is also an attempt on mixing Russian traditional capturing rule with North American king capturing rule, but where a king is supposed to act as long range piece: it is called 'Alaska' or 'Alaskan draughts' : glukkazan.github.io/checkers/alaska-checkers.htm .
I had played hundreds of games in these variants just for fun, and there is one good detail which can't be ignored: under this particular king rule a player who has material advantage, should be able to convert it into win very easy.
Why it is important to know? There are some exceptional draws in English draughts where extra draughtsman or even extra king can't provide a win, however, under North American rule, these exceptional draws don't exist!
Similarly, in variants where a king is long range piece, on 8x8 board 3 kings are mandatory for trapping 1 king. However, when you play 'Alaskan draughts', you will notice that even 1 extra draughtsman provides winning advantage.
Therefore, this rare and unusual capturing rule might lead to very competitive draughts variants.
So, @Rechefiltr_is_Fire , if you want to bring us some innovation, you can use this capturing rule idea and maybe even expand it.

@kalnap is that implementable on Lidraughts? My question was technical)

@Rechefiltr_is_Fire It is implementable, but it would require MANY volunteers, and, given that we can't have engine analysis for variants on 8x8 board which would require less work, it is more unlikely that you will see more variants being implemented in next years.

So please save this discussion and remember when you’ll need…

…bye and wishing good to Lidraughts…

To reply to @kalnap I asked the website's owner and he said Alaskan draughts was a joke

@harris Of course, Alaskan draughts is not originated from native players, but it is pretty good variant: it has much easier endgames then Russian or Pool have. If you are interested to promote this variant, you can change labeling. As well, Pool and North American mixture is also very enjoyable variant.
As for labeling problem, let me note that famous Chinese checkers is not some traditional Chinese game, but there are people who love to play it despite the labeling :)

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