If I understand well, u want to get a pvalue assessing the significance of a correlation.

Using random permutation is a good idea. However you should do the randomization many times in order to have an empirical distribution of the (A,C) correlation. From that distribution, you can then get the significance of your (A,B) correlation.

Good luck !

Edit : The statistical test to use will depend on your distribution. If it is normal (you can use a normality test to make sure of that), then you could compute the mean, standard deviation and pvalue like this (with R) :

#rand_corr = vector of random correlations
#here for testing, 10000 random number with 0.2 mean and 0.2 sd
rand_corr=(rnorm(10000,0.2,0.2))
# pval calculation :
mean <- mean(rand_corr) #mean of random (A,C) correlations
sd <- sd(rand_corr) #sd of random correlation
x <- 0.9 #true (A,B) correlation value
z <- (x-mean)/(sd) #center normalize
2*pnorm(-abs(z)) # return pval
# visual representation :
hist(rand_corr, breaks=30)
abline(v=x, col="red")

However if the normality is not respected (it might not be since you have correlation values that cannot go below 0 or higher than 1), you might need to ressort to other tests.

The topic is misleading, a FDR (false discovery rate) is calculated for a particular p-Value, e.g., using permutation test. Probably, you meant something else?

How do you calculated the correlation between the two BED files? What are you actually comparing, i.e., what kind of entities are in the BED file? Exons? Genes? SNPs?

How exactly did you do the randomization? For each entry in the BED files you randomly selected a value from the interval (-1000; 1000) and added that to the start and end?

Actually I am comparing two CHIPseq peak file. So here I am just comparing coordinates by checking overlap. Suppose if all coordinates of A overlaps with B that we can say correlation is 1. So like that comparison has been done. In order to assess that correlation is significant or not I have randomized coordinates by shifting it to for e.g 1kb upstream or downstream (C). now here my question was how I can say that correlation between A and B is significant compared to A and C. And for that I think P value is needed. I hope I made it more clear.

I'm a bit confused... Do u want to get a pvalue assessing the significance of a correlation ?