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Here is the sentence including the word.
わしはあの東光少年院にはいったが さいご とうてい 生きて 出られるような気がせんのや。
It is said by Kansai spoken guy.
I have tried to look on some Japanese dictionary web sites and found that the word that is close to the meaning in my opinion is 気がせく but I think it cannot be conjugated to the form in the sentence above. The word would be 「気がせない」but I am uncertain about it.
気がせんのや means 気がしないのだ. や would be a Kansai form of だ, and せん is an alternative form of しない. As for why it's not しん, it's derived from せぬ, which in turn is derived from せず.
Nothing at all already explained the question about 気がせんのや, but for your information, related to the last paragraph:
I have […] found that the word that is close to the meaning in my opinion is 気がせく but I think it cannot be conjugated to the form in the sentence above. The word would be 「気がせない」 but I am uncertain about it.
the negative form of せく (急く) is せかない (or せかん if you use the negative ん), not せん or せない.
