If the lines you see are instrumental they should not or only to some extend depend on the nature of your sample. A known problem is reflections and diffraction. Tests to do: sample holder filled with liquid of same refractive index as sample, dilutions of sample.
1. What kind of instrument do you use? What were your experimental conditions, what was the compound that measured? Did you use filters?
2. Pleas attach the spectrum. What is the characteristic of these peaks?
3. The strange bands may be Raman bands. You can verify the Raman-band with the variation of the excitation wavelength (position of Raman-peaks changing with the excitation energy, but the position of fluorescence bands do not)
spectrofluorimeter usually has two monochromator: one in excitation channel and another in registration channel.
There is second-order transmission in monochromators.
For the excitation channel, this leads to not only the passage of light with a wavelength of, for example, 300 nm but also 600 nm. And the 600 nm light will be scattered in the cell and will be recorded as narrowband luminescence.
Similarly, for the registration channel. Luminescence of sample with maximum at lambda gives response with maximum 2lambda in registration monochromator. For example (HQ.jpg), hydroquinone shines in the band of 300-400 nm (lambdaex = 224 nm). At the spectrum you see a narrowband signal at 448 nm and the additional response at 600 - 800 nm.
My suggestion is closely related to the preceding answer by Yurii Tsaplev. Will you check whether the maxima of your strange peaks will shift linearly with the change of excitation wavelength.
I really wonder that no one asks the author to show an example spectrum together with her question. Quite useless to speculate about the possible source of her observation without being able to also see it, right?
Thanks from all who replied my question. according to the answers here as well as my studies, the answer of B. Tsaplev is probably the reason of my question, because the sharp band has been appeared exactly at twice of excitation lambda. So, it can be because of second-order transmission.