I think the sentence should be ”少し眠いかな”. The meaning is "Maybe I'm a bit sleepy".

少し眠い＝sleepy しかな× かな＝？

This old useage of Japanese not rately use now Now can see old japanese liteture means feel like therefore whole sentance mean I'm little feel like asleep ~ しかな　　たのしかな　　feel like interesting (emotion verb +shikana) whrer you find this ?