I estimated DEGs from RNASeq using edgeR method. But the final DEG list has several genes with low counts and are having high Fold change 

             logFC	 logCPM	  F	     PValue	    FDR	      Ctrl1	 Ctrl2	Str1	Str2
    Gene1	7.673	-2.658	33.203	1.27E-05	0.000118	0	  0	  0.738954	0.657007
    Gene5	7.605	-2.951	26.996	3.36E-05	0.000255	0	  0	  0.674697	0.657007
    Gene35	7.499	-2.072	22.724	8.47E-05	0.0034	    0	  0	  0.642569	0.594435
    Gene67	7.462	-2.151	36.849	2.49E-06	3.32E	    0	  0	  0.642569	0.563149

Initialy, I filtered out low count genes using  

    keep<-filterByExpr(y,group = group)
    y<-y[keep,keep.lib.size=FALSE] 

But I am not sure why genes normalized count value close to zero are retained and listed as DEGs. How can I solve this? I was thinking to use min.count parameter in filterByExpr. 
But, is that the right way? Suppose if I use, `keep<-filterByExpr(y,group = group, min.count=500)`, the genes with greater than 1 normalized counts are retained. 

**To be more specific, where should I apply `filterByExpr` function, before normaliztion (ie on raw counts) or after normaliztion** ? 

Code:

    group<-factor(paste(targets$Genotype,targets$Time,targets$Treatment,sep="."))
    cbind(targets,Group=group)
    y<-DGEList(counts = raw_counts, group = group)
    
    #Filterout low count genes
    keep<-filterByExpr(y,group = group)
    y<-y[keep,keep.lib.size=FALSE]
    
    #Data Normalization
    y<-calcNormFactors(y)
    
    #Design matrix
    design<-model.matrix(~0+group)
    colnames(design)<-levels(group)
    
    #Dsipersion estimation
    y<-estimateDisp(y,design)
    fit<-glmQLFit(y,design)


Before normalization (or acutally it does not matter as filterByExp does not consider the normalization since it filters on counts). 

What values do you have in the Ctrl1, Ctrl2, Str1 and Str2 coulmns? CPM? In that case the filtering probably works as gene1 have at least 0.657007 * Xe6 reads in two samples. If you have sequenced 40e6 reads that corresponds to at least ~26 reads in two samples.

That said - if you want a more stringent filtering you just have to apply it yourself.