Sorry, this might seem a late reply as it is already past Diwali. If you have not yet bought one, I did recomend Panasonic fridge. I am using a 418Lts model and it is consuming less electricity than my old BPL 185Ltrs refrigerator. It is 5 start rated model. You should go only for a 5 star rated model and if budget is not a constraint then go an inverter based model, this will consume even less electricity than a 5 srat rated model with normal compressor - Panasonic has got those, iirc Hitachi also has those but they are overpriced ue to the steel finish they got.
Regarding your query about a Fridge consuming les than 1 unit of electricity: I guess that may not be possible in a normal home. If you open/close it a few times only then you may reach that goal but I am quite skeptical about it. All new fridges come with a label which shows nominal elecricity comsumption per year (in terms of units). I think that will come in handy to compare when you go to buy the fridge. Mine for e.g. consumes 582 units/year which comes to 1.52 units/day; which is quite close to your goal. And lastly a frdige will consume less electricuty only if it is kept on 24/7, if you switch it off at night and then switch it back on in the morning, it will consume way too much electricity than it would have, had it been kept ON all the time.