Branches of foreign banks are not allowed.
"Article 12. Bank founders
The founders of the bank can be legal entities and individuals - residents, as well as non-residents.
The state may be the founder and shareholder of the bank represented by the Ministry of Finance of the Republic of Uzbekistan, as well as other state organizations on the basis of decisions of the President of the Republic of Uzbekistan. Enterprises and organizations in which more than fifty percent of the authorized fund (authorized capital) belongs to the state cannot be the founders and shareholders of the bank, unless otherwise provided by law.
[...]
Chapter 2. Minimum conditions for admission to banking
Article 15. Establishment of a bank
Banks are created in the form of a joint-stock company.
Banks receive the status of a legal entity from the moment of their state registration with the Central Bank.
The Bank operates in the Republic of Uzbekistan on the basis of a license for the right to carry out banking activities (hereinafter referred to as the license) issued by the Central Bank.
[...]
Section 17. Additional requirements for foreign founders when they create a bank or participate in the authorized capital of a bank. 
When a foreign bank is created or participates in the authorized capital of the bank, in addition to the documents specified in Article 16 of this Law, the following documents are additionally submitted: [...]
The total share of non-residents - individuals and legal entities that are not international financial institutions, foreign banks and other credit organizations, should not exceed fifty percent of the bank's authorized capital.
The Central Bank has the right to establish minimum requirements for capital and credit rating of the founders of the bank - non-residents who are not international financial institutions, foreign banks and other credit organizations, as well as to the rating of the state of residence of non-residents.
The founders and shareholders of the bank may not be non-residents whose participants (shareholders) and ultimate beneficial owners are registered in the state or in the territory that provide the preferential tax regime and (or) do not provide for the disclosure of the identity of the ultimate beneficial owner and the provision of information during financial transactions.
[...]
Article 30. Branches and representative offices of foreign banks in the territory of the Republic of Uzbekistan
The creation of branches by foreign banks in the Republic of Uzbekistan is not allowed.
A representative office of a foreign bank is a separate subdivision of a foreign bank located on the territory of the Republic of Uzbekistan and representing the interests of the bank without the right to carry out banking and other commercial activities.
A representative office of a foreign bank in the territory of the Republic of Uzbekistan is accredited by the Central Bank. [...]" (LAW OF THE REPUBLIC OF UZBEKISTAN ON INTRODUCING CHANGES AND ADDITIONS TO THE LAW OF THE REPUBLIC OF UZBEKISTAN “ON BANKS AND BANKING ACTIVITIES” No. ZRU-580 of 11/05/2019 [google translation])
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"Article 2. Banking entities
Subjects of banking activities are all banks established in the Republic of Uzbekistan.
[...]
Article 3. Basic concepts [...]
foreign bank - a legal entity that is a bank under the laws of the foreign state in whose territory it is registered;
[...]
Article 5. Licensing of bank activities
The bank, including foreign ones, operates in the Republic of Uzbekistan on the basis of a license issued by the Central Bank of the Republic of Uzbekistan. The license specifies the list of operations performed by the bank.
Banking activities carried out without a license are considered illegal, and income received as a result of such activities is subject to seizure to the state budget.
[...]
Article 7. Founders of the bank
Banks are created, as a rule, in the form of a joint stock company based on any form of ownership.
The founders of the bank can be legal entities and individuals, including foreign ones, with the exception of government bodies, public associations and public funds, unless otherwise provided by law.
See  previous  edition.
The maximum share of participation of each shareholder in the authorized capital is established by law.
The acquisition of bank shares is carried out in the manner prescribed by law.
The bank's founders do not have the right to resign from the bank's shareholders within a year from the date of its registration.
Participation of a bank in the authorized capital of other banks is not permitted, except for cases of creation of banks with the participation of foreign capital and subsidiary banks, as well as other cases provided for by law.
[...]
Article 10. Registration and licensing of banks' activities
Banks receive the status of a legal entity from the moment of their registration with the Central Bank.
The procedure and conditions for registration are established by the Central Bank.
Simultaneously with registration, banks are issued a license to conduct banking operations.
Registration of banks and issuance of licenses to them is carried out for a fee.
Bank branches are registered with the Central Bank and operate on the basis of a license issued to the bank that created them.
[...]
Article 15. Additional requirements for the establishment and activities of banks with foreign capital participation
The Central Bank has the right to establish additional requirements for banks with foreign capital, including requiring foreign banks to confirm that the bank is under the supervision of the control body at its location and registration.
Licenses to foreign banks are issued only if the bank of a foreign state has the right to accept cash deposits and other valuables in its country on repayment terms.
Article 16. Branches and representative offices of banks
Banks can open branches in the Republic of Uzbekistan, and banks of foreign countries can open representative offices with the permission of the Central Bank.
A bank branch is a separate division that carries out banking activities on behalf of the bank that created it.
A representative office of a foreign bank is a separate division that represents its interests and does not carry out banking activities.
The heads of branches are appointed by the head of the bank that created them in agreement with the Central Bank.[...]" (LAW OF THE REPUBLIC OF UZBEKISTAN ON INTRODUCING CHANGES AND ADDITIONS TO THE LAW OF THE REPUBLIC OF UZBEKISTAN “ON BANKS AND BANKING ACTIVITIES” No. № 216-I of 25.04.1996, as amended [google translation])
LAW OF THE REPUBLIC OF UZBEKISTAN ON INTRODUCING CHANGES AND ADDITIONS TO THE LAW OF THE REPUBLIC OF UZBEKISTAN “ON BANKS AND BANKING ACTIVITIES” No. ZRU-580 of 11/05/2019 [google translation]
LAW OF THE REPUBLIC OF UZBEKISTAN ON INTRODUCING CHANGES AND ADDITIONS TO THE LAW OF THE REPUBLIC OF UZBEKISTAN “ON BANKS AND BANKING ACTIVITIES” No. № 216-I of 25.04.1996, as amended [google translation]
[<a href="https://lex.uz/docs/4581971">Law</a>],[<a href="https://lex.uz/docs/12011?ONDATE=04.10.2018">Law</a>]