Question: Which branch of the Indo-European language family does this language belong in which Kalyi Jag means "Black Fire?"

Context paragraphs:
Italo-Celtic: In historical linguistics, Italo-Celtic is a grouping of the Italic and Celtic branches of the Indo-European language family on the basis of features shared by these two branches and no others.  There is controversy about the causes of these similarities.  They are usually considered to be innovations, likely to have developed after the breakup of the Proto-Indo-European language.  It is also possible that some of these are not innovations, but shared conservative features, i.e. original Indo-European language features which have disappeared in all other language groups.  What is commonly accepted is that the shared features may usefully be thought of as Italo-Celtic forms.

Lydian language: Lydian was an Indo-European language spoken in the region of Lydia in western Anatolia (present-day Turkey).  It belongs to the Anatolian group of the Indo-European language family.

Sinhala numerals: Sinhalese belongs to the Indo-European language family with its roots deeply associated with Indo-Aryan sub family to which the languages such as Persian and Hindi belong.  Although it is not very clear whether people in Sri Lanka spoke a dialect of Prakrit at the time of arrival of Buddhism in Sri Lanka, there is enough evidence that Sinhala evolved from mixing of Sanskrit, Magadi (the language which was spoken in Magada Province of India where Lord Buddha was born) and local language which was spoken by people of Sri Lanka prior to the arrival of Vijaya in Sri Lanka, the founder of Sinhala Kingdom.  It is also surmised that Sinhala had evolved from an ancient variant of Apabramsa (middle Indic) which is known as ‘Elu’.  When tracing history of Elu, it was preceded by Hela or Pali Sihala.

Kalyi Jag (group): Kalyi Jag (Romani for "Black Fire") is a Hungarian Romani folk music group.

Illyrian languages: The Illyrian languages are a group of Indo-European languages that were spoken in the western part of the Balkans in former times by groups identified as Illyrians: Ardiaei, Delmatae, Pannonii, Autariates, Taulanti (see list of ancient tribes in Illyria).  Some sound changes from Proto-Indo-European to Illyrian and other language features are deduced from what remains of the Illyrian languages, but because there are no examples of ancient Illyrian literature surviving (aside from the Messapian writings if they can be considered Illyrian), it is difficult to clarify its place within the Indo-European language family.  Because of the uncertainty, most sources provisionally place the Illyrian language family on its own branch of Indo-European, though its relation to other languages, ancient and modern, continues to be studied.

Caucasian Albanian alphabet: The Caucasian Albanian alphabet, or the alphabet for the Gargareans, was an alphabet used by the Caucasian Albanians, one of the ancient and indigenous Northeast Caucasian peoples whose territory comprised parts of present-day Azerbaijan and Daghestan.  It was one of only two indigenous alphabets ever developed for speakers of indigenous Caucasian languages (i.e. Caucasian languages that are not a part of larger groupings like the Turkic and Indo-European languages families) to represent any of their languages, the other being the Georgian alphabet.  The Armenian language, the third language of Caucasus with its own alphabet, is an independent branch of the Indo-European language family.

Indo-Aryan languages: The Indo-Aryan or Indic languages are the dominant language family of the Indian subcontinent.  They constitute a branch of the Indo-Iranian languages, itself a branch of the Indo-European language family.  Indo-Aryan speakers form about one-half of all Indo-European speakers (about 1.5 of 3 billion), and more than half of all Indo-European languages recognized by "Ethnologue".  While the languages are primarily spoken in South Asia, pockets of Indo-Aryan languages are found to be spoken in Europe and the Middle East.

Punjabi language: Punjabi ( ; Gurmukhi: ਪੰਜਾਬੀ "pañjābī" ; Shahmukhi: "paṉjābī" ) is a native language of the Punjab region belonging to the Northwestern Indo-Aryan branch of the Indo-European language family.  Spoken by over 100 million native speakers worldwide, it ranks as the 10th most widely spoken language (2015) in the world.  It is the native language of the Punjabi people, who associate with the historical Punjab region of India and Pakistan.  Among Indo-European languages, it is unusual in having lexical tone.

Romani language: Romani ( , , or ; also Romany, Gypsy, or Gipsy; Romani: "romani čhib" ) is any of several languages of the Romani people belonging to the Indo-Aryan branch of the Indo-European language family.  According to Ethnologue, seven varieties of Romani are divergent enough to be considered languages of their own.  The largest of these are Vlax Romani (about 500,000 speakers), Balkan Romani (600,000), and Sinte Romani (300,000).  Some Romani communities speak mixed languages based on the surrounding language with retained Romani-derived vocabulary – these are known by linguists as Para-Romani varieties, rather than dialects of the Romani language itself.

Tocharian languages: Tocharian, also spelled Tokharian ( or ), is an extinct branch of the Indo-European language family.  It is known from manuscripts dating from the 6th to the 8th century AD, which were found in oasis cities on the northern edge of the Tarim Basin (now part of Xinjiang in northwest China).  The discovery of these languages in the early 20th century contradicted the formerly prevalent idea of an east–west division of Indo-European language family on the centum–satem isogloss, and contributed to re-invigorated study of the family.  Identifying the authors with the "Tokharoi" people of ancient Bactria (Tokharistan), early authors called these languages "Tocharian".  Although this identification is now generally considered mistaken, the name has stuck.

Supporting paragraphs: Kalyi Jag (group) Romani language
Answer: the Indo-Aryan branch