I'm not sure what's causing that, but here are a few edits you can try out. You can either edit the enbseries.ini file with a text editor, or (on recent ENBs) use the in-game menu. Either back up the original file, or use comments to track the original settings (if manually editing), using the double slashes, like I use below.
Is this happening from armor? If so, look at the specular settings (try setting them to 0.0, or 1.0 max). If not, the first thing I'd try is the LenzReflection settings. Set them to between 0.0 and 1.0. LenzReflection can create very extreme lens flare effects if set very high, and many configs leave the values at or near 0.0.
[BLOOM]
AmountDay=1.0
ContrastDay=1.0
[CAMERAFX]
LenzReflectionIntensityDay=0.1 // or 0.0
LenzReflectionPowerDay=1.0
[ENVIRONMENT]
SpecularAmountMultiplierDay=1.0
SpecularPowerMultiplierDay=1.0
SpecularFromLightDay=0.0