Of the two, only 걸리는데 is correct. 걸리는데 is 걸리다 (hang, catch or trip over something) conjugated with -는데 ("but" or "given that ..."). -(으)ㄴ데 is a similar conjugation but it only applies to adjectives. Verbs and adjectives behave similarly in Korean, but they diverge in these present tense forms. Here are some examples of how they conjugate differently. - 영철이가 저기 온다 (오다 -> 온다 - 'ㄴ' is added to the base for present tense verbs) - 영철이는 행복하다 (행복하다: adjective's present tense form is the same as the base form) - 일을 하는 사람 (하다 -> 하는. -는 is the present tense modifier form of verbs). (말하는 소리, 끓는 물, 내리는 비) - 피곤한 하루 (피곤하다 -> 피곤한. -(으)ㄴ is the present tense modifier form of adjectives. (긴 줄, 큰 차, 밝은 방, 넓은 집) -는데 in 걸리는데 is a similar case of present tense conjugation as 하는. -(으)ㄴ데 form only applies to adjectives, and makes no sense with verbs. (There is a two word phrase 걸린 데 (=걸린 곳 = where something is hung/caught), but I doubt this what you're refering to).

If you spelled '걸린데' wrong, I assume you might hear this word '걸린대'. '걸린대' is short for '걸린다고 해'. '걸리다' means 'to take time to do something'. '-다고 해' is used to deliver the message you heard from someone else to the listener. e.g. 캐나다에서 한국까지 비행기로 열세 시간이 걸린대. (I heard it takes 13 hours by plane from Canada to Korea.)