peculiarity

noun3

1. •
   The state or quality of being peculiar; individuality; singularity.

   • The peculiarity of meeting six people on a usually deserted trail only struck me later on.
2. •
   That which is peculiar; a special and distinctive characteristic or habit; a particularity.

   • I had often heard of Miss Marchmont, and of her peculiarities (she had the character of being very eccentric), but till now had never seen her. — 1853
3. •
   Exclusive possession or right.