Behold, the third time I am ready to come to you; and I will not be burdensome to you: for I seek not yours, but you: for the children ought not to lay up for the parents, but the parents for the children.
The third time - (see 'Introduction' to 1 Corinthians.) His second visit was probably short (1 Corinthians 16:7), and attended with humiliation through the scandalous conduct of some (cf. 2 Corinthians 12:21; 2 Corinthians 2:1). It was probably paid during his three years sojourn at Ephesus, from which he could pass so readily by sea to Corinth (cf. 2 Corinthians 1:15-16; 2 Corinthians 13:1-2). The context implies nothing of a third preparation to come; but, 'I am coming the third time, and will not burden you with my maintenance this time, anymore than I did at my two previous visits' (Alford). It could be of no moment, in connection with 'I will not burden you,' whether he once or twice was ready to go, but whether he had actually been with them several times already.
Not yours, but you (Philippians 4:17).
Children ... parents. Paul, as their spiritual father (1 Corinthians 4:14-15), does not seek earthly treasure from them, but lays up the best treasure (namely, spiritual) 'for their souls' (2 Corinthians 12:15).