Let’s divide this question into two areas - 1947-1966 and 1975-1987

Both periods were periods during which Yugoslavia did seek nuclear weapons but, for various reasons, didn’t actually get very close.

We start with Pavle Savic, Serb Physicist. During the late thirties, Savic was based in Paris at the Radium Institute during which time he assisted with discoveries that would eventually lead to nuclear fission. He was also an active communist and, after being deported from France, joined the Partizans. Post-war, he led the scientific push for Yugoslavia to set up a nuclear institute (that would become Visca) and spent time dealing with Soviet scientists to set this up. Come 1948 and the split between Tito and Stalin, Savic’s plans stalled as he could no longer bring in Soviet expertise and would essentially have to restart from scratch. Visca would be set up in Belgrade with institutes in Zagreb and Ljubljana but the level of co-operation between was poor as state secrecy from above hindered communication. To solve this, Aleksandar Rankovic was placed in charge of the nuclear commission overseeing all three sites.

Rankovic was, of course, also the head of the secret police. Under his rule, small research reactors would be built but there was also turnover of scientists with some even being forced into exile. Further complicating matters was a resource issue - Yugoslavia didn’t have much in the way of uranium so research was focused on plutonium. Come the mid-sixties, Rankovic fell from favour (he had left the nuclear institute a few years earlier but had put a chosen man in charge) and, without his drive behind the bomb effort, the move to neutrality took prominence.

Until 1974 and India, another non-aligned state, tested their bomb. With that having been done, Tito changed his mind again on the bomb - specifically running a civilian programme alongside a military one. The former (along with finding more uranium) would result in the construction of the Krsko plant. The latter can very much be TL;DRd - Yugoslavia didn’t have the money to make a real push to get it and, towards the later 80s, divides in the scientific community (SANU, Vojko I Savle) further holed efforts.

It’s fair also to note turnover again - Yugoslavia was a founder member of CERN but left in 1961 and part of the decision to leave was because their experts were leaving the nation for CERN.

Yugoslavia’s nuclear story is, in short, a series of efforts that received terminal setbacks - losing Soviet expertise, turnover of domestic scientists, resource issues and non-alignment all played big parts in removing impetus.