You may try some other excitation wavelength where the background emission is minimum.

You can use a cuvette with smaller pathlength. Smaller pathlength will have smaller background emission. In the same time in order to have same absorbance (as in longer pathlength cuvette) you have to increase the sample concentration. So the inner filter effect here will decrease the intensity of the background emission in presence of your enzyme.

If your sample absorbance is very low (less than 0.05) then simply substract the background emission from sample emission spectra. However, if the sample absorbance is high inner filter effect caused by the dye will decrease the background emission in the sample spectra. Thus when you try to subtract it, some part of the spectrum might go negative. If absorbance is high, try this. Measure the emission of the ionic liquid solvent (say, IIL). Note down the absorbance (Adye) at the excitation wavelength after addition of the dye. Now multiply IIL with 10^(-Adye/2). Subtract  this inner filter corrected background spectra from the dye spectra. It should  give a close value of the dye spectra.

I would suppose that in studying enzyme structure in a certain solvent, its concentration is generally very low. So, fluorescence of a background solvent might be so high that its subtracting could lead to a final small difference of large values which is problematic. Perhaps, the suggestion by Dr. Tuhin Khan, to check various excitation wavelengths might indeed help. 

Thank to dear Tuhin and Mikhail

The problem is about fluorescence emission of the ligand which overlaps with enzyme's emission. There should be a way to subtract the ligand's emission from the total. Is there a formula to calculate this subtraction?

You can try my previous suggestion itself. Consider ligand emission instead of background emission.

I am going to study the enzyme's intrinsic fluorescence. I tried 275, 280, and 295 nm wavelengths. The ligand emitted in these three wavelengths. Besides, I don't use a dye. So ... By the "dye", you mean ionic liquid?

And please tell me your e-mail address dear Tuhin.