Hi,
Some things come into my mind:
You have to understand the "turn_off_voltage" of a bjt. It specifies the voltage at a dedicated collector current. It does not say, that at lower V_BE the collector current is zero.
And you have to understand the "leakage_current" of a bjt. It usually is specified at V_BE is zero.
And you have to understand that your requirement uses a V_BE somewhere inbetween those two specified transistor states, thus you can expect a collector current inbetween the two specified values.
This is a very unusual requirement, thus you rarely will find information about it in the datasheets.
This leads to my question:
Why do you want to use the bjt especially in this situation?
* Why don't you drive V_BE close to zero ... to avoid increased collector current?
* Or if impossible, why don't you use a collector connected circuit that is less sensible for the increased collector current?
If you post your circuit you could get more helpful answers.
Klaus
Added:
I really cannot say about the leakage.
This makes no sense for me: Complaining about "too high current" but not having a clue what "too high" means.
In my eyes: A proper design starts with deciding the requirements. After that you start to design the schematic ... not the other way round.