'을께' is a standard pronunciation of '을게', but you should write '을게' according to 맞춤법. There is no difference in meaning and writing "을께" instead of '을게' is a common mistake Korean learners make.
There are two types of consonants, one is 'fortis (strong in Latin)' and the other is 'lenis (weak in Latin)'. Sometimes they are identified with "tense and lax".
A weak consonant such as 'ㄱ' is pronounced as a strong consonant 'ㄲ' when a certain 받침 (final consonant in a block) is used.
According to 표준발음법 (Standard Pronunciation), 제 6장 (Article 6), 27항 (Section 27):
관형사형 ‘-(으)ㄹ’ 뒤에 연결되는 ‘ㄱ, ㄷ, ㅂ, ㅅ, ㅈ’은 된소리로 발음한다.
할 것을 [할꺼슬], 갈 데가 [갈떼가], 할 바를 [할빠를], 할 수는 [할쑤는], 할 적에 [할쩌게], 갈 곳 [갈꼳], 할 도리 [할또리], 만날
붙임] ‘-(으)ㄹ’로 시작되는 어미의 경우에도 이에 준한다.
할걸 [할껄], 할밖에 [할빠께], 할세라 [할쎄라], 할수록 [할쑤록], 할지라도 [할찌라도], 할지언정 [할찌언정], 할진대 [할찐대]
It is very important to note that some final consonants in a block could change the pronunciation that follows it. It is called "경음화 (Tensification where a weak consonant is pronounced as a strong consonant)"