In addition to "on the premises" and "in the premises," you could say "at the premises."
"At" in this case is used to indicate a point in a general vicinity, like the "at" in "She's at the office," or, I'll meet you at the restaurant."
Google shows 75,600 examples of "at the premises," as in these examples:
"¢ ... must not assault, molest, harass, threaten or otherwise interfere with the protected person(s). 2. The defendant must not reside at the premises at which the ...
www.lawlink.nsw.gov.au/lc.nsf/pages/AVO%20complaint - Similar pages
"¢ ... That such officer(s) shall make a detailed inventory as to the property seized,leaving a copy thereof at the premises, as well as personally serving a copy on www.usdoj.gov/usao/eousa/foia_ reading_room/usam/title6/tax00025.htm
Google shows 70,200 examples of "at the [adjective] premises":
"¢ ... exhibitor. GENERAL STAND REQUIREMENTS. Adhesive, pins, nails or Velcro must not be used on any wall at the exhibition premises. Any ...
"¢... The reporting of cattle movements shall be the sole responsibility of the receiving premises or person responsible for the animals at the receiving premises
. usaip.info/USAIPCattlereport.ppt ...
The preposition to use with "the premises" – in, on, or at – appears to follow the usual patterns for the prepositions of place.