The line is translated there as 'troubled kids is the last thing I need'. The word has nothing to do with the biological meaning of عجان, which is pronounced 3ijaan not 3ijjaan. The singular is apparently originally عجي, from a different root entirely. According to the Syrian Culture Ministry Dictionary this word originally means orphans raised badly.
The idiomatic construction you need to get this line is ناقصني كذا؟ which literally means 'am I missing X?' but should be understood as 'I have enough trouble without...' I don't know the word عكنّي for absolute certain, but I intuitively understand it as synonymous with simple كنّي kinni 'as if I'm', which again has to be understood idiomatically here. You could translate the line as 'as if I don't have enough problems without the worries (humum) that troubled kids bring with them'. This pairs with the previous lines where he's talking about black sheep (this metaphor exists in English too so I assume it also exists in Hebrew) who've run away from the fields.
I think you can understand the whole song as a weary father tired of life talking to his son, if this helps.