i checked with non inverting amplifier circuit in LTC6268IS8-10#PBF amplifier that non inverting input is 100MHZ sinewave from Oscillator .output is unstable and noise for 1.5 to 9 gain value
I would not recommend using a pot (VR1) in the feedback loop of a High Speed amplifier like the LTC6268. I'd instead use a SMT fixed resistor with absolute minimum lead / trace length and loop area.
Also, SMA CN2 on your schematic should be properly terminated to ground (e.g. 50ohm to ground) near U3 (assuming you've plugged a coax onto CN2?).
In addition, your V- (-2.5V supply) should be adequately decoupled as you've done with your +2.5V (C54, C55) supply, if not already.
These may help with the instability you're observing?
I think the opamp U3 does not have the required DC bias current return path, see this article for explanation: https://www.analog.com/en/analog-dialogue/articles/common-problems-when-designing-amplifier-circuits.html
You can solve the problem by connecting a resitor between pin 3 of the opamp and ground. 1k should be OK.
As far as I understand the original problem has been solved. In my opinion the DC shift and gain problems are mainly caused by two things:
Both affect the stability of the opamp. Just make an LTSpice simulation of the amplifier part of the circuit. Put a capacitor at the output (say 5pF to 10pF to represent the probe) and another one in parallel with the feedback resistor (the VR1 pot may have parasitic capacitance of about 10pF or so). I did so, and I got just what you have observed: positive DC shift and anomalous gain. A parasitic oscillation appears with a frequency over 800MHz, so you do not see it on an oscilloscope with much less bandwidth. Even the PCB layout can be critical.
I tried with LTspice 100MHZ Input but is not Level shifting and In Practical I'm using TPP1000 Probe also i observed in both Function generator and 100MHZ oscillaotor output is Level shifting for same circuit in LTspice but If i set 10MHZ sinewave input in functional generator output is fine amplifying
I have found some values for correct operation at 100MHz. I think it is important to have a series resistor at the output to isolate the capacitive load of the probe. It seems to work fine, if in the feedback loop the capacitance is not higher than 2pF (at least for this situation, gain=2). I think this can be a starting point for you to find proper values for all gains you'd like to use and then make a PCB carefully that can maintain the stability and proper operation. Here is the result of the simulation:
As you can see, it works fine for 100MHz sinusoidal input.