Using dplyr, you can select the first 400 records for each value of year using group_by and slice. Then create quantiles, either within each year or overall.
set.seed(911) # Simulate some uneven data
df <- data.frame(year=rep(2016:2018, times=c(400,500,600)),
                 val=rnorm(1500,50,5))
library(dplyr); library(tidyr)
This creates quantiles within each year
df %>% group_by(year) %>%
  slice(1:400) %>%
  mutate(q4 = cut(val, 
                  breaks=quantile(val, 
                                  probs = seq(0,1,1/4)), 
                  include=TRUE, labels=FALSE)) %>%
# You can stop here and save the output, here I continue to check the counts
  count(q4) %>%
  pivot_wider(names_from=q4, values_from=n)
# A tibble: 3 x 5
# Groups:   year [3]
#   year   `1`   `2`   `3`   `4`
#  <int> <int> <int> <int> <int>
#1  2016   100   100   100   100
#2  2017   100   100   100   100
#3  2018   100   100   100   100
Or you can ungroup to create overall quantiles (counts will differ per year).
df %>% group_by(year) %>%
  slice(1:400) %>%
  ungroup() %>%
  mutate(q4 = cut(val, 
                  breaks=quantile(val, 
                                  probs = seq(0,1,1/4)), 
                  include=TRUE, labels=FALSE)) %>% 
# Stop here to save, or continue to check the counts
  group_by(year) %>%
  count(q4) %>%
  pivot_wider(names_from=q4, values_from=n)
# A tibble: 3 x 5
# Groups:   year [3]
#   year   `1`   `2`   `3`   `4`
#  <int> <int> <int> <int> <int>
#1  2016   116    88   102    94
#2  2017    86   114    85   115
#3  2018    98    98   113    91