っこない is a combination of the 接尾語（せつびご） (suffix) っこ, and the い-Adjective ない. When attached to the 連用形（れんようけい） (masu-stem form) of verbs, it creates new い-Adjectives that express the impossibility of (A). (A) being whichever verb is used.
Common translations of っこない include ‘there is no chance of (A)’, or ‘doing (A) is impossible’.
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今年（ことし）中（じゅう）に30万円（まんえん）貯（た）めたいの？お前（まえ）の給料（きゅうりょう）じゃできっこないよ。
You want to save up 300 thousand yen this year? There is no chance you can with your salary.
どんなに鍛（きた）えてもあの人（ひと）だけには勝（か）てっこないよ。
No matter how much I train, there is no chance that I can beat him.
あんなデカい家（いえ）、どんなに貯金（ちょきん）しても買（か）えっこないよ。
I will not be able to buy a house that big, no matter how much I save.
Caution - Although extremely rare, as っこ stems from the kanji 子（こ）, this grammar point may occasionally be seen in its kanji form.
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明日（あした）までに５ページのレポートとか、絶対（ぜったい）書（か）けっ子（こ）ないよ。
There is no way that I can write a 5 page essay by tomorrow.
こんな漢字（かんじ）だらけの新聞（しんぶん）なんて読（よ）めっ子（こ）ない。
There is no way I can read this newspaper that is filled with kanji.