Canto 2 -
Ayodhyā-kāṇḍa
Chapter 8: The Conversation Between Kaikeyī and Mantharā
Text 2.8.7

प्रत्यासन्नक्रमेणापि भरतस्यैव भामिनि।
राज्यक्रमो विप्रकृष्टस्तयोस्तावत्कनीयसोः॥

pratyāsanna-krameṇāpi bharatasyaiva bhāmini
rājya-kramo viprakṛṣṭas tayos tāvat kanīyasoḥ

pratyāsanna-krameṇa = by the order of proximity [by birth]; api = even; bharatasya = Bharata; eva = alone [should get the kingdom]; bhāmini = O beautiful woman; rājya-kramaḥ = [The possibility of] the kingdom being attained; viprakṛṣṭaḥ = remote; tayoḥ = by the two; tāvat = is actually; kanīyasoḥ = younger [sons Lakṣmaṇa and Śatrughna].

O beautiful woman, even by the order of proximity [by birth], Bharata alone [should get the kingdom]. [The possibility of] the kingdom being attained by the two younger [sons Lakṣmaṇa and Śatrughna] is actually remote.

Mantharā presents another argument for why Rāma is afraid of Bharata alone [among His brothers]: by the order of Their proximity by birth, that is, by the order of their birth nakṣatras Punarvasu and Puṣya, Bharata alone should get the kingdom.

According to her, dependent sons are equally desirous of taking over the kingdom [like their non-dependent brothers], but the first claim for the kingdom is to Rāma, then to Bharata and then to Lakṣmaṇa and Śatrughna. She thought that therefore Rāma hated Bharata [and not the remaining two].