There are many ways to do it, here is one.
amst <- matrix(c(52.37, 4.88), ncol=2)
points <- data.frame(longitude=..., latitude=..., anything=..., else=..., here=...)
some_limit <- 3000 # defaults to meters
inside <- geosphere::distHaversine(amst, points[c("longitude","latitude")]) < some_limit
points[inside,,drop=FALSE] # all points inside
But ultimately this incomplete answer would be much better informed when you provide sample data. Your previous efforts and perhaps some context are best informed by you showing any code you've tried; sometimes lack of code suggests "please code this for me for free", though that can often be jumping to conclusions when you have no idea.
Here is complete MWE, using a 30km radius around Amsterdam.
library(maps)
library(mapdata)
library(ggplot2)
library(geosphere)
neth <- map_data('worldHires', 'Netherlands')
amst <- data.frame(long=4.88, lat=52.37)
n <- 500
set.seed(2)
points <- data.frame(
long = amst$long + runif(n, min=-1, max=+1),
lat = amst$lat + runif(n, min=-1, max=+1)
)
some_limit <- 30000 # meters
points$inside <- distHaversine(amst, points) < some_limit
ggplot() +
geom_polygon(data=neth, aes(x=long, y=lat, group=group)) +
coord_fixed(1.3) +
geom_point(data=amst, aes(x=long, y=lat), color='green', size=5) +
geom_point(data=points, aes(x=long, y=lat, color=inside))
