1. I have a digitally controlled resistance series network.
2. What I have done is placing a resistor at output terminals of each relay. I have 6 relays.
Whenever i need that resistor I turn off the relay, whenever I need to bypass the resistor I turn on the relay so effectively giving short.
3. Using normal SPST 12V sugar cube relay.
4. Problem is when i turn on relay with 12V coil, the relay turn on resistance at output terminals starts increasing gradually & then finally settles to around 2 ohms.
5. This 2 ohms resistor effects by circuit.
6. How do remove that or I have to use some other solution?

 

http://www.electronicoscaldas.com/datasheet/JQC-3FC(T73)DC12V_JIHJIK.pdf

this is relay I am using.

Relay have following written on it:
HL
JQC-3FC(T73)DC12V

 

Give us the schematic so we can see exactly how you have got things connected as my Crystal ball needs a polish and I've sent it off for a service

 

Attached is the circuit. This is how I add multiple relays in series.
Whenever I have take resistance value I turn off relay so path completes through that resistance.
In case I do not need resistance I turn on the relay , effectively giving 0 ohms in that circuit.
This is how I make multiple resistor value.

I am using multimeter to measure resistance value. maximum current will be 3A through these resistor.

Problem was relay resistance keeps on increasing, if I turn it on(upto 2ohms). Thus adding large resistor errors in final computational resistance.

I had checked some signal relays where contact/weeting current is low. But still I had found that its 10ma minimum. Again multimeter pass much less current.

So what alternative should I use instead of relays?

 

Your problem is that relays are not designed to have reliable, repeatable, resistance across the contacts. They are only designed to have insignificant resistance compared to the load they are meant to switch power for. I think you need some MOSFETS. They are very predictable, especially if you give them a good, solid, 10V to 12V on their gate and then measure the results and calibrate to that. Why calibrate? Because the wires and connections will contain a few tenths of an ohm, even if you are very good at your assembly work.